ame no hi ha karada ga darukute, nanimo sitakunaikoto ga arimasu.

の links two nouns.

• 雨 = rain
• 日 = day

So 雨の日 literally means a rain day, or more naturally, a rainy day / a day when it rains.

This is a very common pattern in Japanese:

• 夏の日 = a summer day
• 休みの日 = a day off
• 日本の映画 = a Japanese movie / a movie from Japan

In this sentence, 雨の日は means as for rainy days or on rainy days.

The は marks 雨の日 as the topic of the sentence.

So the sentence is structured like:

• 雨の日は = as for rainy days
• 体がだるくて、何もしたくないことがあります = my body feels sluggish, and there are times when I don’t want to do anything

This does not mean rainy days are the grammatical subject in the English sense. It means the speaker is saying, speaking of rainy days...

A very natural English translation is:

• On rainy days, ...
• When it’s rainy, ...

Here, が marks 体 as the thing that has the state だるい.

• 体がだるい = the body feels sluggish / I feel physically sluggish

Using が is very normal with adjectives describing a state, especially when something specific is being identified as having that state.

Why not は?

• 体がだるい sounds like a straightforward description.
• 体はだるい would sound more contrastive, like my body is sluggish, but... or as for my body, it’s sluggish.

So が is the more natural choice here.

Also, in Japanese, 体がだるい often just means I feel physically sluggish. It does not need to sound as literal as my body is sluggish in English.

だるい means something like:

• sluggish
• languid
• physically heavy
• worn out
• listless

It is not exactly the same as 疲れている (tired).

• 疲れている focuses more on tiredness or fatigue.
• だるい often suggests a heavy, unmotivated, physically off feeling.

So on a rainy day, 体がだるい suggests a kind of dull physical sluggishness.

だるくて is the て-form of the い-adjective だるい.

For い-adjectives, you make the て-form by changing い to くて:

• 暑い → 暑くて
• 寒い → 寒くて
• だるい → だるくて

Here, だるくて connects to the next part of the sentence:

• 体がだるくて、何もしたくない
• I feel sluggish, and I don’t want to do anything

It can mean a simple connection like and, and sometimes it also suggests a reason or background:

• because I feel sluggish, I don’t want to do anything

In this sentence, both ideas are possible, and the nuance is very natural.

したくない comes from する (to do).

The pattern is:

• する = to do
• したい = want to do
• したくない = do not want to do

So:

• 何もしたくない = I don’t want to do anything

This 〜たい form expresses the speaker’s own desire very naturally. It is most commonly used for:

• I want to...
• I don’t want to...

So in this sentence, it sounds natural because the speaker is talking about their own feeling.

何も is commonly used with a negative verb to mean:

• nothing
• not anything

So:

• 何もしたくない = I don’t want to do anything

This is a very common grammar pattern:

• 何もない = there is nothing
• 何も見えない = I can’t see anything
• 何も食べたくない = I don’t want to eat anything

A key point: 何も usually goes with a negative expression.

Here, こと turns the preceding clause into an abstract thing / occurrence / case.

So:

• 何もしたくないことがあります = there are times/occasions when I don’t want to do anything

This is related to the common pattern:

• verb / clause + ことがある

which often means:

• there are times when...
• sometimes...

So this sentence is not saying there is a literal physical thing. The こと is making the idea not wanting to do anything into an event/case that can exist.

Yes, 何もしたくないときがあります is also natural.

The difference is roughly:

• 〜ことがあります = there are occasions/cases when...
• 〜ときがあります = there are times when...

ことがあります can sound a little more general or abstract. ときがあります points a bit more directly to actual moments in time.

In many everyday situations, the difference is small, and both are understandable.

Because こと is not a person or animal. It is treated as a non-living, abstract thing/event.

In Japanese:

• あります is used for things, events, and abstract existence
• います is used for people and animals

So:

• ことがあります = there are occasions / it happens sometimes

Using います here would be incorrect.

No. The ending ことがあります shows that this happens sometimes, not every time.

So the nuance is:

• On rainy days, there are times when I feel sluggish and don’t want to do anything.
• Sometimes on rainy days, I feel sluggish and don’t want to do anything.

If the speaker wanted to say this always happens, they would use a different structure.

It is omitted, which is very normal in Japanese.

Even though the sentence says:

• 体がだるくて = the body feels sluggish

it is understood from context that the speaker means:

• my body feels sluggish
• or simply I feel sluggish

Japanese often leaves out subjects and possessors when they are obvious from context. So a native speaker would naturally understand this as talking about the speaker’s own condition.

It is a mix that is common in everyday Japanese writing and speech.

• だるくて is not specifically polite; it is just a connective form.
• あります is polite.

So the sentence ends politely because of あります.

A plainer version would be:

• 雨の日は体がだるくて、何もしたくないことがある。

A more casual spoken version might also be expressed in slightly different ways, but the original sentence is perfectly natural and polite enough for general use.