1993 GMC Sonoma catalic convertor

converter could be stopped up causing these issues or timing could even be off causing symptoms.

Could the coil or the distributor have anything to do with the problem?

possible but should throw the check engine light on

If I remove th e cat would that fix the problem?

removing converter is never a good thing to do because it will effect emissions as well as MPG of vehicle and will also make check engine light remain on. you wouldn't pass emission testing if required in your area with a removed converter..

By changing my cat would that fix my problem with the engine not staying on

if the cat. is indeed clogged then yes

I just changed the cat on my truck but its still not working right. It was a bad cat but it didn't solve the problem. Got any ideas on what could it be?

check compression in cylinders , timing may be off which would cause the cat. to get hot and engine to not run .

How do I check compressionin the cylinders? Is it too hard to do? Would that fix the timing or do I need to get that checked out too

it's not hard to do, you just need a compression gauge. if its low on all cylinders than it is a good indication that timing may be off. follow this link to learn how to check compression https://www.2carpros.com/dia/how_to_check_compression.htm