Recently I was doing a show for my school and massive feedback occurred. Next thing you know the mic stopped working because the batteries didn't work. The batteries were brand new at the beginning of the show. The broken batteries were replaced, and the mic worked again. All other mics worked fine with the new batteries till the end of the show.

My question is, could the feedback have anything to do with the mic not working/batteries being dead.

Yes, most certainly.

In normal use, with no sound into the microphone, the current drawn from the battery is quite low.

With sound into the microphone the current increases.

I both cases the internal circuit is simply an amplifier driving a very low powered transmitter.

When acoustic feedback occurs, the microphone is part of an oscillatory loop and the current taken from the battery increases dramatically.

I have an Asus F3 laptop and it appears the battery is dead after just over 2 years. I need to plug my machine in - in order for it to work. I am going to buy a new battery - however before I do that could it be something else that's wrong or does it sound glaringly obvious that it's the battery?

well, in my opinion, when u first got your new laptop and battery, the work time is different from the performace your battery play now. full charge the laptop battery and compare with the work time, if it is over half of the new one, you should change it. for most battery can be normal used in 400-500 charge and discharge circles.

I have a Swiffer Wet Jet and the batteries are dead. I can't find the battery compartment anywhere on the thing. Do you know where they are?
YES thank you James!

the battery compartment is right under the where to bottle of cleaning solution goes…there is a little grey tab that will open the compartment

I've never seen a laptop that can hold a charge for more than 2 hours. Mac users tell me their lap top batteries go on all day on 1 charge.

Apple has rules for programming that release unnecessary information and processes instead of holding them. At least this is true for the iPhone, which is programmed in a light version of the framework used by OSx. This allows the software to run more efficiently and has something to do with battery life. There are of course other factors, but this is one thing.