I didn't realize you had a distributor. I would go ahead and replace the distributor cap. Wouldn't worry about oem for that part either, it's not a mechanical part. Pick one up at any local parts store, swap it over and see if that helps. If it doesn't, just return it. Just the cap, mind you. But take the cap off and inspect the gap of the contacts and make sure no moisture has made its way in there.
The cap looked good, no moisture in it at all. My boyfriend has been looking over the wires and whatnot while I was working and said they're all looking good.
Side note, apparently other vehicles in the same parking lot as my vehicle are having the issues. We got a lot of rain mind you, but mine at least sounds like it's trying to start, their vehicles aren't even trying to turn over.