I just acquired a Peavey Transtube Bandit 112, but it has a few issues that need fixing, however, I am no electronics guru and I don't really know where to start other than looking for loose connections.

Basically, the volume is very very low, almost inaudible, but there definitely is sound coming out of the speaker. I have tried the cord and guitar another amp and they both work fine, so its definitely a problem with the amp.

Probably a Loose connection between the speaker and the circuit board.
Take it to a guitar/amp tech.

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I checked the connection between the speaker and circuit and it wasn't loose, but I reconnected them anyways, issue is still the same.
I would also check the cable comming from the input jack from inside your amp, sounds like a bad or loose connection somewhere, also maybe the powertube got damaged and needs replacing?
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check the inputs/outputs/headphone/line out-ALL THE JACKS!!!-for any debris(i.e.broken 1/4" jacks)dont be scared to look inside of the amp either(just assuming).look for cracked solder joints and repair any you find.these are the most common types of failures and are easily solved.

i might be able to help more if i knew more details.such as:what sound comes out of the speakers when it its audible,settings during the occurences.and anything else you think might help.just PM me.