39k miles and all stock. Battery is new but sometimes when I turn the key it will not crank but all accessories turn on. 24 hours later it fires right up without hesitation. What can I check? Fuses must be fine if it cranks up, I cleaned the chip on the key. Maybe starter or wires?

Ignition switch?
Here'* the full manual.

https://charm.li/Buick/1996/Regal%20V6-3.8L%20VIN%20K/

Time to start troubleshooting!

When you start, is power getting to the starter relay?

If so, is power getting to the starter solenoid?

If so, is there a click?

Etc.

I've checked all the fuses and they are good. The battery cables are all attached and so is the connection to the starter. Where can I find this relay to test? I do have a voltmeter. Thanks.

From pages 6-53 through 6-59 of your owner'* manual:



Personally, I would check for voltage at the starter solenoid first.

How are you checking fuses to see if they are good or not?

Testing with a voltmeter or test light. I like using a simple test light and do it like this.
can do an entire fuse box in a minute or two.