Learn Hardcore Russian: Включённый телевизор мешает мне засыпать. - The TV that is on prevents me from falling asleep.

It comes from the perfective verb включить (to switch on).
Formation: включить → включённый (switched on, turned on).
It behaves grammatically like an adjective: it agrees in gender, number and case with the noun телевизор (masculine, singular, nominative).

So включённый телевизор literally means “the switched-on television / the television that is switched on.”

Why is it включённый телевизор and not телевизор включён?

Both are possible, but they work differently:

Включённый телевизор мешает мне засыпать.
Here включённый directly modifies телевизор like an adjective. You’re describing what kind of TV is causing the problem (the one that is on).
Телевизор включён и мешает мне засыпать.
Here включён is the short form participle used as a predicate, like “The TV is on and is disturbing me.”

Nuance:

Включённый телевизор… sounds more compact and slightly more “written”/descriptive.
Телевизор включён… sounds more like stating a fact about the TV first (“The TV is on”) and then adding the effect.

Both are correct; the original just packs the description into a single noun phrase.

Is включённый passive or active? Why not something like включающий телевизор?

Включённый is passive, not active.

включить – to switch on (perfective).
включённый – that has been switched on (by someone).

So включённый телевизор = “TV that has been turned on” (it underwent the action).

An active participle would be:

включающий – switching on (doing the action).

Включающий телевизор would mean “the TV that is switching on [something]”, which makes no sense here. That’s why the passive form включённый is used.

Why does включённый end with -ый and not something like -енным / -ённым?

Russian full passive past participles often end in -нный / -тый / -тый but then can shorten to an adjectival form when used attributively.

Formally, from включить you get:

participle base: включённ-
full participle: включённый (masc. nom. sg.)

This -ый is just the regular masculine nominative adjective ending attached to the participle stem включённ-:

masc. nom. sg.: включённый телевизор
fem. nom. sg.: включённая лампа
neut. nom. sg.: включённое радио
plural nom.: включённые приборы

So -ый shows gender/case; the participle stem itself is включённ-.

Why do we use мне and not меня after мешать?

Because мешать in the sense “to disturb, hinder” takes the dative case:

мешать кому? чему? — to disturb / to bother whom? what?

Мне is the dative of я:

я (I) → мне (to me, for me)

So:

Телевизор мешает мне. – The TV bothers me.
Музыка мешает ему. – Music bothers him.
Шум мешает соседям. – Noise bothers the neighbors.

Using меня (accusative/genitive) here would be ungrammatical with мешать in this meaning.

What is the pattern мешать кому-то делать что-то? How does мешает мне засыпать work grammatically?

The common pattern is:

мешать + dative (кому?) + infinitive (что делать?)

Meaning: to prevent / disturb someone from doing something.

Examples:

Шум мешает мне работать. – Noise prevents me from working.
Свет мешает ребёнку спать. – The light bothers the child when he’s sleeping.
Телефонные звонки мешают нам сосредоточиться. – Phone calls prevent us from concentrating.

In your sentence:

мешает – he/she/it hinders
мне – to me (dative)
засыпать – to fall asleep (infinitive)

So literally: “The turned-on TV hinders me to fall asleep” (i.e. from falling asleep).

Does мешать always mean “to disturb”? I’ve also seen it mean “to mix.”

The verb мешать has two main, unrelated meanings:

To disturb, hinder, bother (what we have here)
- Grammar: мешать кому? чему? (dative) + optionally an infinitive.
- Example: Ты мне мешаешь. – You’re bothering me / You’re in my way.
To mix, stir (e.g. food, liquids)
- Grammar: usually мешать что? (accusative) or мешать что с чем.
- Example: Мешать суп ложкой. – To stir the soup with a spoon.

Context tells you which meaning is intended. In your sentence, only the “disturb” meaning makes sense.

Why is the infinitive засыпать used and not заснуть?

Both relate to “falling asleep,” but they differ in aspect:

засыпать – imperfective: to be in the process of falling asleep, to fall asleep in general/habitually.
заснуть – perfective: to fall asleep once, to manage to fall asleep (a completed event).

With мешать, the imperfective infinitive is most natural when you talk about an ongoing ability or process:

мешает мне засыпать – disturbs the process of my falling asleep in general / every time.

If you say:

мешает мне заснуть – it hinders me from (finally) falling asleep (this specific time, reaching the result).

Both are grammatically correct, but:

засыпать – more about the process; sounds more general/habitual.
заснуть – more about achieving the state once; sounds like “I can’t get to sleep (this time).”

What is the difference between засыпать and спать?

засыпать – to fall asleep, to begin sleeping (the transition from awake to asleep).
спать – to be sleeping, to be in the state of sleep.

Compare:

Мне мешает засыпать свет. – The light prevents me from falling asleep.
Мне мешает спать свет. – The light prevents me from sleeping (it wakes me up / doesn’t let me stay asleep).

In your sentence, the focus is on starting to sleep, so засыпать is used.

Why is включённый masculine and in the nominative case?

Because it agrees with телевизор, which is:

телевизор – masculine, singular, nominative (it’s the subject of the sentence).

Adjectives and participles must match their noun in:

Gender (masculine/feminine/neuter),
Number (singular/plural),
Case (nominative/accusative/etc.).

So we get:

включённый телевизор – masc., sg., nominative.
If the subject were feminine or plural, включённый would change:
Включённая лампа мешает мне засыпать. – The turned-on lamp…
Включённые телевизоры мешают мне засыпать. – The turned-on TVs…

How is включённый pronounced, and why is there ё instead of е?

Pronunciation: [вклю-чён-ный], with stress on -чён-.

ё is always stressed and pronounced as [yo] in Russian.
The spelling включённый clearly marks that stress and sound.

In ordinary Russian texts, writers often omit the two dots and write е instead of ё, so you may see включенный. But:

It is pronounced the same as включённый.
Dictionaries and textbooks normally keep ё to show proper pronunciation and stress.

Can I change the word order, e.g. Включённый телевизор мне мешает засыпать or Мне мешает засыпать включённый телевизор?

Yes, Russian word order is flexible, and all of these are grammatical:

Включённый телевизор мешает мне засыпать.
Включённый телевизор мне мешает засыпать.
Мне мешает засыпать включённый телевизор.

They all mean roughly the same, but the focus shifts:

Version 1 (original) is neutral: first describe the TV, then say what it does.
Version 2 puts a slight emphasis on мне (“to me, personally”).
Version 3 puts emphasis on включённый телевизор as the thing causing the problem (especially in contrast to something else).

In everyday speech, 1 and 3 are the most typical.

Could we drop включённый and just say Телевизор мешает мне засыпать?

Yes, you can. Then the meaning is simply:

Телевизор мешает мне засыпать. – The TV (in general, as a thing) keeps me from falling asleep.

Adding включённый gives a more precise idea:

It’s not “the existence of a TV set in the room” that bothers you.
It’s explicitly the fact that it is turned on (sound, light, etc.).

So включённый clarifies why it bothers you.