Learn Hardcore Korean: hyudaepon baeteoriga eobseoyo.

Because 없다/없어요 takes a subject marked with 이/가. The structure is “X이/가 없다” = “X doesn’t exist / there is no X.” So 배터리가 없어요 means “(There is) no battery.” Using 는/은 would make it a topic and add contrast (see below).

What’s the difference between 배터리가 없어요 and 배터리는 없어요?

배터리가 없어요: Plain statement that there’s no battery (or the battery is dead).
배터리는 없어요: Topic/contrast. “As for the battery, there isn’t (but maybe something else is).” You use 는/은 to contrast with something previously mentioned or implied.

Why is there no 의 between 휴대폰 and 배터리?

Korean often drops 의 in noun–noun possession when the relationship is obvious. 휴대폰 배터리 naturally reads as “phone battery.” 휴대폰의 배터리 isn’t wrong, but it sounds heavier and is more common in careful/technical writing.

Can I drop the particle and say 휴대폰 배터리 없어요?

Yes. In casual speech, subject particles 이/가 are often omitted when the meaning is clear. 휴대폰 배터리 없어요 is natural in conversation. Keeping 가 is a bit more precise or careful.