Did you check to make sure your getting fuel? I just had a problem with my integra somewhat similiar to yours. It cranked strong but wouldnt always start. When it did start ran fine. After a week of sporadic starting, i pulled the cap, and checked the primary coil (zero ohms). Put cap back on and car refused to start. You may have damaged the coil further, or initially if you cranked with the cap off due to what ive read. Ive also heard people recommend changing the ignitor and coil together since a new one may blow the other due to the increase of efficiency. Listen to Worleybot too, there are crankshaft angle sensors etc that cant be replaced individually. If you still suspect the distributor, I would just replace the whole distributor for around 220 with a total brand new unit like i just did yesterday(esp if you have high miles). If you need any help just ask. Ive had to research this problem for the last week and im sure our cars are very similiar. Everyone just told me it was the MFR although I told them it definitely was not that.
---Oh wait a minute, just reread your post. Sounds like your problem could be caused by the coolant reaching the cylinders. If thats mixing with the combustion, well its gonna run like sh** and probably not that long. I would get your head gasket etc checked out asap.