Rough starts

I bought my xj about a month ago, and it's always started fine until the day before yesterday. The day before, my exhaust rotted out at the muffler inlet. I got that sleeved and welded. I don't think it's connected, but later that night leaving work (about 32 degrees) I hit the key like I normally would and it didn't catch right away like normal. I hit it again, and it cranked like I would think it would when a battery was dying, but it started, barely running, I hit the gas and got it up to idle, and it was fine after that. I drove 4 miles home. I figured my battery was weak, and the 5 minute McDonalds run I made earlier didn't help it.

The next afternoon, figuring my battery was on it's way out, I went out to start it. It cranked over, caught, and immediately stalled out. Cranked again, and while it felt like it had enough juice to turn it over, it didn't seem like it was doing it with the same authority it normally does. Same thing again where it barely ran until I gave it some gas, then it was fine. I started it twice more later in the evening a few hours apart, and it started up fine. It still felt like the started wasn't turning the motor as fast as it normally does, but that just may be me trying to justify my original thoughts.

After it's running, there is nothing strange to speak of. It drives and idles as normal. The voltmeter is showing pretty consistent 14v, there are no warning lights. The fuel pump sounds strong when I turn the key to run. I have not checked the plugs, but the wires and cap appear to be relatively fresh. Starter looks pretty new, but it got a used car dealer engine bay cleaning so it could just be that it's old and washed. Battery is a 600 Mopar of unknown age.

Any thoughts?

Started like normal both times I drove today. Hoping I just had some sort of isolated fluke problem, but I'm sure as soon as I forget about it the problem will resurface and be worse.

Here's what I would do: clean battery connections, clean grounds, and clean connections at starter. If symptoms persist, charge the battery overnight and have it tested at a parts store.

I debating on whether to just buy myself a battery for Christmas, because I know I'll need one eventually and I would rather do it when I sort of have the money, rather than when I don't. At the same time, I hate replacing something I don't need to. Granted, it'd be an upgrade, but yeah.

Everything went fine again today.

Battery connections are clean as a whistle, could stand to check them anyway as well as grounds and the starter, but it's cold and I hate the cold.

Yeah it is no fun to work on something if it is too cold

I shouldn't really complain. The past few winters have been pretty mild in Michigan.

I've been able to tough it out wearing shorts on the 4 mile drive to work. It's pretty warm in the building, and I'm pretty active, hence the shorts in December. If it stays above freezing, I can handle being outside in shorts for a few minutes.