Yeni dizüstü bilgisayarım eskisiyle eşdeğer.

A natural breakdown is:

• yeni = new
• dizüstü bilgisayar = laptop computer
• bilgisayarım = my computer
• eskisiyle = with the old one / to the old one
• eşdeğer = equivalent, of equal value

So the sentence means something like:

My new laptop is equivalent to the old one.

A more literal gloss would be:

My new laptop [is] equivalent with the old one.

Turkish often uses with-type marking where English uses to in this kind of sentence.

-ım is the 1st person singular possessive suffix, meaning my.

So:

• bilgisayar = computer
• bilgisayarım = my computer

Turkish usually shows possession by adding a suffix directly to the noun, instead of using a separate word like my.

Other examples:

• kitap = book

• kitabım = my book

• telefon = phone
• telefonum = my phone

Because of vowel harmony and consonant changes, the possessive suffix can appear in different shapes, such as -ım, -im, -um, -üm.

Dizüstü bilgisayar is the normal Turkish term for laptop.

Literally:

• diz = knee
• üstü = its top / upper part / on top of
• dizüstü = on the lap
• bilgisayar = computer

So dizüstü bilgisayar literally corresponds to something like lap computer.

In everyday Turkish, people also sometimes just say:

• laptop
• notebook (less common, depending on context)

But dizüstü bilgisayar is a standard native Turkish expression.

Eskisiyle means with the old one or, in more natural English here, to the old one.

It is built from several parts:

• eski = old
• -si = a suffix meaning something like the one that is old / the old one
• -yle = with

So:

• eski = old
• eskisi = the old one / his-her-its old one / the old version
• eskisiyle = with the old one

In this sentence, eskisi refers to the previously mentioned thing: the old laptop.

English often uses the old one, and Turkish commonly does this by turning an adjective into a noun-like form.

Because eski by itself is just the adjective old.

To say the old one, Turkish usually adds a nominalizing/possessive-type ending:

• eski = old
• eskisi = the old one

Then you can add case endings:

• eskisiyle = with the old one
• eskisine = to the old one
• eskisinden = from the old one

So eskiyle would not sound right here if you mean with the old one as a noun phrase. You need eskisiyle.

Yes, ile means with, and it can be written separately or attached.

So these are equivalent:

• eskisi ile
• eskisiyle

The attached form is very common in normal writing and speech.

A few examples:

• arkadaşı ile = arkadaşıyla = with his/her friend
• benimle = with me
• seninle = with you

When attached, ile often changes shape slightly:

• ile → -le / -la / -yle / -yla

Which form appears depends on pronunciation and vowel harmony.

Eşdeğer means equivalent, of equal value, or comparable in worth/function.

It is a bit more formal or technical than simply saying the same.

So:

• eşdeğer = equivalent
• aynı = the same

These are not always identical in meaning.

For example:

• Bu ilaç öbürüyle eşdeğer.
  = This medicine is equivalent to the other one.
  It may not be literally the same item, but it has the same effect or value.

• Bu ilaç öbürünün aynısı.
  = This medicine is exactly the same as the other one.
  This suggests stronger sameness.

In your sentence, eşdeğer suggests the new laptop matches the old one in value, level, or capability.

There is no separate word for is here because Turkish often omits the present-tense copula in third-person nominal sentences.

So:

• O doktor. = He/She is a doctor.
• Bu güzel. = This is beautiful.
• Yeni dizüstü bilgisayarım eskisiyle eşdeğer. = My new laptop is equivalent to the old one.

This is completely normal Turkish.

If you change tense, then a visible copular form can appear:

• Yeni dizüstü bilgisayarım eskisiyle eşdeğerdi.
  = My new laptop was equivalent to the old one.

So in the present tense, third-person is/are is often just understood.

The word order here is very natural:

• Yeni dizüstü bilgisayarım = topic/subject
• eskisiyle = comparison phrase
• eşdeğer = predicate

Turkish is flexible, but the most neutral order usually puts the main predicate at the end.

So this version is standard:

• Yeni dizüstü bilgisayarım eskisiyle eşdeğer.

You might change the order for emphasis, but the tone changes:

• Eskisiyle yeni dizüstü bilgisayarım eşdeğer.
  This is possible, but it sounds more marked or contrastive.

For learners, the safest choice is to keep eşdeğer at the end.

Yes. Yeni modifies the noun phrase dizüstü bilgisayarım.

So:

• yeni dizüstü bilgisayarım = my new laptop

In Turkish, adjectives normally come before the noun they describe:

• yeni kitap = new book
• büyük ev = big house
• eski araba = old car

Here, the full noun is dizüstü bilgisayarım, and yeni goes before it.

In this sentence, eskisi means the old one, and the context tells us it refers to the old laptop.

Turkish often avoids repeating the noun when it is already clear.

So instead of saying something longer like:

• eski dizüstü bilgisayarıyla

Turkish can simply say:

• eskisiyle

This is very natural and efficient. English does the same with the old one.

That version is not correct if you mean equivalent to my old laptop, because eski dizüstü bilgisayarımla means with my old laptop, and the possessive reference becomes awkward here.

If you want to say the full version explicitly, you would more naturally say something like:

• Yeni dizüstü bilgisayarım eski dizüstü bilgisayarımla eşdeğer.

This can be grammatically interpretable as My new laptop is equivalent to my old laptop, but it sounds heavier and less natural than eskisiyle.

In real Turkish, eskisiyle is preferred because it avoids unnecessary repetition.

So the original sentence is the most natural choice.

It sounds a little formal or technical because of eşdeğer.

In everyday conversation, people might more often say something like:

• Yeni dizüstü bilgisayarım eskisi gibi.
  = My new laptop is like the old one.

• Yeni dizüstü bilgisayarım eskisi kadar iyi.
  = My new laptop is as good as the old one.

• Yeni dizüstü bilgisayarım eskisiyle aynı seviyede.
  = My new laptop is at the same level as the old one.

But eşdeğer is perfectly correct and natural in the right context, especially when talking about value, function, performance, or technical equivalence.

You would add the past copula:

• Yeni dizüstü bilgisayarım eskisiyle eşdeğerdi.
  = My new laptop was equivalent to the old one.

Here:

• eşdeğer = equivalent
• -di = was

This is useful because it helps show that the present-tense version has an understood is, even though no separate verb appears.

A rough pronunciation guide is:

yeh-nee dee-zoo-stoo bee-lee-sigh-yah-rum es-kee-see-yle ehsh-deh-er

A few notes:

• yeni = yeh-nee
• dizüstü has rounded vowels: dee-zoo-stoo
• bilgisayarım is approximately beel-gee-sigh-yah-rum
• eskisiyle flows together smoothly: es-kee-see-yle
• eşdeğer is roughly esh-deh-er

The exact sounds are more precise than English spelling can show, but that gives a helpful approximation.