96 Lumina takes couple minutes to start

Hello, I have a 1996 Lumina with a V6 3.1 motor. It has 134,000 miles on it. The problem is when the car is cooled off and I try to start the car it wont crank. However if I wait 5 minutes, the car will start fine. The battery seems to be fine and is only two years old. I thought it was the starter and replaced it yesterday. After I replaced the starter yesterday I started it about 15 times throughout the day and thought the problem was fixed until I went out to the car this morning only to find not starting again. Waited 5 minutes and it started fine. The car will keep starting fine until it cools back down. I have no idea what could be wrong. The problem seems to be getting worse becacuse it used to not happen every time the car got cold but now seems to be happening more often. I had the intake manifold replaced a month ago and the problem happened once before that. Thanks for any help.

Edit:

I started timing the length of time when the car will not start. It has been exactly 3 minutes every time. I have done it 4 times and the amount of times I try to start the car within the 3 minutes doesn’t seem to matter. I have tried to start the car at 2:58 and it wouldn’t start and couple seconds later it started fine. This only happens when the car has been sitting for a couple hours. It starts fine when its warmed up.

When you say it wont crank does it just click once, or click multiple times, or is there a click at all? Try turning on headlights when it will not crank and hit the starter, do the headlights go out? Have you tried jumping it as soon as the problem come about?

When you say it wont crank does it just click once, or click multiple times, or is there a click at all? Try turning on headlights when it will not crank and hit the starter, do the headlights go out? Have you tried jumping it as soon as the problem come about?
When I turn the key the computer comes on and all the lights on the dash come on. The engine doesnt make any sounds. The first time this happened, I jumped the car but that took 10 min to get everything together so I bet it would have started anyway. I did turn on the headlights and try to start the car and they stayed bright.