I ran out of gas a few blocks away (ironically, on my way to the gas station) and had to walk home and refill it. It gave me a little trouble but then started OK.

At the gas station, it didn't start for a half an hour. Some guy tried to jump it for me, but the battery seems to be fine; if anything, working too well, since the clock on the dash won't turn off when I take the key out.

The engine doesn't even turn over, it just kind of makes a click noise. If I hit start on the remote starter and put in the key, it sometimes starts up, but that's like a 50/50 chance.

anyone ever deal with anything like this?

If I hit start on the remote starter

Thats your problem