Car wont start unless battery is disconnected first

2003Pontiac Grand Am GT, 3.4L V6…It only starts if the battery has been disconnected for at least an hour and then is immediately reconnected prior to use. Once the block is hot, however, it starts flawlessly and repeatedly every time. When the block cools, it won’t start again unless I disconnect the battery and wait an hour.

What are the presenting symptoms? Does it do nothing, “click,” turn over slowly, cough+stumble, etc.

Has the battery been load tested? How old is it? Did you try swapping in a known good battery? That’s where I’d start. I’m suspecting a marginal battery that can spin the engine fast enough when the oil’s up to temp and the job is easier, but fails at the harder job of a cold start. Without more info, though, I’m just guessing.

First order of business: rule in/ rule out battery health. Once that’s done, progress onward.

If the starter is working then I would suspect a problem within the ignition circuit.