3rd Cylinder Not Firing

I have a 89 skyline gt. Turbo... The car ran great the few times I test drove it. The day after I bought it I drove it pretty hard but nothing extreme. It rode fine. The next day I start it up it's shaking and soundin pretty down and out. I went to the garage and killed off each plug. I found out the 3rd cyl. isn't firing. When I first start it up in the morning the car runs okay for about 5 minutes tops (the 3rd is doin it's job) Then it acts up again. I though hmmm spark plugs? Kinda weird then I thought coil packs? Then about the unit mounted on the engine that runs to the packs. My question is where should I start and how much should I expect to spend?

Where are you located?

I am pretty sure I can seel you one pretty cheap.

Coil packs. Common problem.

My Skyline Did The Same I Brout A Brand New Coil Pack And Ignition Module Still Droped A Cyl. Waste Off $$ I Pulled Out The Plugs And Didnt Like What I Saw It Had Melted The Tips Off Repaced The Plugs Then It Burned A Pretty Hole In The Exaust Valve Apperently Its A Fuel Problem (leans Out When Hitting Boost)