Bad distributor? or just bad cap and rotor?
 

My 96 civic ex has been sitting for a good 8 months due to a bad transmission, which I just changed this week.
prior to the swap he car turned on right after I changed the alternator, however it shut off on its own while it was oh idle.
today I wanted to do a tune up. The sparkplugs were changed as well as the wires. One of the sparkplugs was burnt at the tip fairly badly. I removed the distributor cap and attempted to remove the rotor, but I realized I was given the wrong parts. I put the cap back on. It is dusty within the distributor cap with a rust color dust.
I put the cap back on and the car started well and idled good for about 5 minutes, then the engine started losing power at time and it almost turned off on several occasions. I turned it off and the car would start again 10 minutes later. It cranks and engine turns, but it dent start.
any ideas on whether is the distributor itself or just the cap and rotor?