I started up and drove it for 10 minutes this morning, then I came home parked it, and tried starting it 5 minutes later. The motor cranks strongly, but won't start.

First thing I thought of was maybe the fuel pump switch got tripped off, so I looked in the trunk but did not find one, and the owners manual does not mention one.

Doesn't this 93 bonneville have a fuel shutoff switch?

Assuming it does not have a fuel shutoff switch - what kind of checks should I do? The battery is new, just a few days old, so the engine cranks strongly. (We just bought the car and had to replace the old battery which was going bad).

Cold start OK, hot start hard is a symptom of a bad Fuel Pressure Regulator. Pull the vacuum line from the FPR and look for evidence of gasoline - if wet - it'* bad.

Lots of other stuff for no start. Check for spark and fuel, loose connections and grounds on sensors and ICM.

Calling for better help for you now.

Have you been able to start "cold", again?

Also, if you turn the key to "ON" (not "START"), can you hear the fuel pump humming (priming)?

If you don't hear anything, the fuel pump may be bad or going bad after the car warms up.

Not starting is usually either no spark or no fuel...so, we need to start eliminating possibilities.

Not sure about a fuel cut-off switch.

there is no cut-off switch with the exception of the VATS...when the security light is illuminated the Fuel pupm will not prime

Had a similar problem in my dad'* 2001 Regal. After much investigation, turned out to be loose electrical connector at the fuel pump. Make sure you check all of the connections. Also, check to ensure that you are getting fuel at the fuel rail (by depressing the schrader valve).

just had olil change and they changed fuel filter, now it has probs starting every time it seems like

For the cost of a fuel filter, I would change it again or call the place and request a different one put on. It is possible that either the new filter is restricted and defective.