Will your computer battery keep your computer from working even when plugged in?

Computers don't have batteries so I'm assuming you're talking about a laptop. Laptops with their battery SHOULD work when its plugged in. Some laptops can even work WITHOUT the battery but still plugged in.

However, if your battery has a critical flaw (dead short) then even with it plugged in, it won't work. I suggest you try the laptop with the battery removed. If it works, that is the problem, otherwise, your laptop has other problems.