Riding Lawn mower nightmare. Please help?

I will provide as much detail as possible. Everything was fine until I did my annual oil change on my 14.5 hp Briggs and Stratton yardman. This mower is about 6 yrs old. I used about half a quart of 20-50w oil and 1 quart of 10-30w. I just wanted to use up the 20-50 and I didn't think it would be an issue. I'm not sure if what followed was coincidence or as a result of that. My mower started to stall after several minutes of use and wouldn't restart. After the engine cooled it would start back up again. The problem got progressivly worse until it wouldn't start at all. I am getting spark and gas. The fuel filter is clean, the spark plug is new and I bought and replaced the air cleaner. So all of the easy stuff is out of the way. I took apart the intake and sprayed some carb/choke cleaner into the carb, put everything back together and whammo, it worked. I ran it for about 15 minutes and it didn't stall. I thought all was well. It started to rain, I turned it off and the next day it wouldn't start again. Dead battery. I replaced the battery, it started right up, I ran it for about 4 minutes and it stalled again. Now it won't start at all again. I since replaced the oil with 10-30w. What is bl**dy blazes do I do now. I have limited mechanical knowledge and I did about all I feel comfortable doing. A buddy of mine keeps telling me he thinks it's the coil. Is that the cylinder shaped part that looks like a large oil filter? I really need ya'lls help here.

Thanks,
Tom