My car stares at me when it's cold, too. It's a very cold stare.
:laugh_ti:
Ok, all jokes aside, it sounds like the ECT might be the culprit. You really need to read the codes and post them so we can get a better idea of what's happening.
The oil pressure sender is not related to this issue.
Have you checked the IAC/IAB? It's the silver cylindrical-looking thing on the intake right off the throttle body with a two-wire connector on the aft end of it. If that's unplugged or dirty (more likely), the car will have trouble starting.
Other culprits could be, yes, the Air Charge Temperature sensor (the one in the airbox), a bad/dirty MAF (If you can't remember the last time you cleaned it, you need to), or maaybe a problem in spark/fuel, but I doubt that.
The ECT is the more aft (or the one to the right, if you're looking at it from the driver's side) of the two coolant sensors. The one on the left is the one-wire that feeds your dash gauge. The one on the right (the one you need the 1" deepwell socket to install) is the one that feeds the ECU.
Once again, though, read the codes. A KOEO should be sufficient; it will tell you if any sensors are out of range.
