88 FC turns on then off. burning oil??
 

I'm new to this but here goes. When I start 88 FC convertible(238k miles) it stays on for a couple seconds, then turns off. Also, I see white smoke come out of the exhaust. I'm sure it's not flooded, I've done the unflooding process multiple times. the smoke that somes out when unflooding comes out and thats it; the smoke out of my car is continuosly coming out. the smoke doesn't smell like gas. I brought a friend over to check on the engine when I started and he saw smoke come out of the oil cap. He open it and there was smoke. My friend, rx8 owner, and I don't know what to do.

how's the coolant level?

The coolant level is/stays full,I also notice smoke coming out of the air pump.

Well I know mine blows a little smoke when it first starts up but that doesn't explain who it won't stay running..