[Corvette95]

Since it seems you are a relative new ZR-1 owner. recommend reading all the tech-tips on your Z. Guessing and throwing parts at it will make a much harder to verify the root cause of the issue. I would forget removing alarm (unless it is an approved GM part). I recommend getting a factory service manual and a good Tech1A from Ebay when they show up. You bought a 30 year old supercar. When it doesn't start do the headlamps dim (try cranking at night or dark garage). Put an amp multi-meter on the starter. Sounds like you are suffering a low battery or NSS or worn starter. It is very normal to have multiple dash lights on after jumper car with low battery. Gotta pay to play. Just the way it is. Follow service manual to the letter when testing with Tech1A.