I have a 1986 Coupe in cherry condition with only 30K.  I recently broke down about 100 miles from home and had to have he car towed to a GM dealership. The problem was found to be the fuel pump which was replaced. 

Perhaps there is a problem with the fuel pump relay. If the relay doesn't close, or the contacts aren't allowing enough voltage across, the pump will not run until the oil pressure comes up. It's a redundant system. If the oil pressure goes below a specified pressure, it turns the fuel pump off, keeping you from driving the car with no oil pressure. My '85 suffers from the same malady....I'm just too lazy to fix it, since it does always start after a few seconds. I'm just not sure if my issue is with the pump relay, or the oil pressure sender unit.
It's just another idea that could be checked.

I had this very same issue a few years back.  Would start fine when it sat overnight, but hard to start again afterwards that day.  I had recenetly changed the spark plugs at that time and noticed that one was wet, not with oil but with gasoline.  Immediately thought it was a leaky fuel injector.  I soon after replaced the injectors and no more problem starting.  Starts up immediately and also runs stronger now.  Sometimes the fuel injectors build up varnish on the pintle and do not close all the way, reulting in a gas leak into the intake runner.  If your 1986 has the original fuel injectors this could very well be the problem.  There is also a ninth injector on the 1986, that's the "Cold Start Valve".  That could be leaking, or the sensor that allows it to open when cold may be malfunctioning and allowing it to open when it shouldn't or possibly not allowing it to open if needed, like when the engine may be warm but not warm enough to start without the extra fuel it injects.  Kind of like a choke on a carburator.  Hope this helps you find the problem.  Let us know how it works out.

Thanks to you all for your suggestions.  I think I will start by installing new injectors and spark plugs. If that doesn't work then I'll look at the fuel pump relay.  I don't think it has anything to do with the oil pressure though but maybe.

I think the above recommendations are probably the most valid, just don't forget about the fuel filter...

[QUOTE=The Car Whisperer]I had this very same issue a few years back.  Would start fine when it sat overnight, but hard to start again afterwards that day.  I had recenetly changed the spark plugs at that time and noticed that one was wet, not with oil but with gasoline.  Immediately thought it was a leaky fuel injector.  I soon after replaced the injectors and no more problem starting.  Starts up immediately and also runs stronger now.  Sometimes the fuel injectors build up varnish on the pintle and do not close all the way, reulting in a gas leak into the intake runner.  If your 1986 has the original fuel injectors this could very well be the problem.  There is also a ninth injector on the 1986, that's the "Cold Start Valve".  That could be leaking, or the sensor that allows it to open when cold may be malfunctioning and allowing it to open when it shouldn't or possibly not allowing it to open if needed, like when the engine may be warm but not warm enough to start without the extra fuel it injects.  Kind of like a choke on a carburator.  Hope this helps you find the problem.  Let us know how it works out.[/QUOTE]

i would get the injectors that the car calls for. my 90 calls for 22# injectors and i installed 24#. was told after a while that eventually it would burn out catalytic converter. besides that the computer can make adjustments at an idle for the extra fuel but at higher speeds it cant adjust it as fast and you wind up using more gas which these days means a lot of money wasted. the only way i can think of to get around that problem would be to have the computer updated with the higher pound injectors.

Yes, I just bought a set of new 22 psi Borsch injectors on Ebay. FYI, the seller said look the VIN. If the eighth digit is an 8 the 22 psi injector will be the exact replacement required and matches the OEM injector. I'm having a hard time finding the ninth injector you refer to as the cold start injector. Is it a switch?  i found a cold start switch. Is this what I need? I also bought an upgraded fuel filter too.