I own a '98 Concours and love it. It has approx. 55K on it and was a one-owner vehicle and regularly serviced. For my own piece of mind (and your recommendations), I took it to our wonderful caddy dealer recently and had the tranny serviced, radiator serviced, Mobil 1 change, new fuel filter and an injection cleansing.
It runs beautiful, but has been experiencing trouble starting once in a while. It happened before and after service and only happens when I shut it off and try to restart a minute to 30 minutes later. It turns fine, but just doesn't seem to be getting the gas. It revs up a bit like it's going to go, but then it just about, or does, peter out. I am concerned I am going to be left stranded somewhere one of these days!
Have the fuel pressure tested.
If the pump is going bad, it will not be getting enough pressure to start the engine up, but will run and drive fine. Also, there may be a leak in the line causing the fuel to drain out while its sitting.
My S10 Blazer had a similar problem, gradually got worse and yes, it was the fuel pump.
In the Blazer the in tank filter (kind of like a nylon sock) had split and pieces of nylon were getting sucked into the pump and wearing it quickly. The pressure dropped noticeably over a couple of weeks while I was diagnosing it.
First thing to check, verify the fuel filter was replaced!!
When the S10 wouldn't start I'd give a shot of starting spray into the air inlet and it would start right up. If it gets worse try that. If it starts everytime with starter spray you know it's not getting enough gas to start.
The interesting thing is it'll run good, even have good power, just not want to start.