Problem is as stated.
Long story short, sometime around September/early Oct I didn't drive this car for 3-4 weeks. Then when I went to drive it, it wouldn't start. Completely dead, no sound at all. This in itself has been a recurring problem for a while now; a couple of times, even after only two weeks of inaction (mild/warm weather) it wouldn't start, even after getting a new (but cheap) battery. There are some interesting details to this that I'd like to share, to aid speculation on something that has plagued me for years, but I'm trying to keep this short. Suffice it to say such things have caused me to wonder if I perhaps have some inherent problem with my old car (or after-market alarm wiring; there are some clues that this might be a problem) which drains and/or damages a battery.
One of the tires also has a slow leak (that I could've sworn existed before I had the tire replaced last), but I can't really afford to delve into the problem and rarely drive anyway, so I just fill it up every few months or so when it becomes noticeably low. Unfortunately, this time it sat there dead for long enough that the tire went flat flat, and has been that way for a month or more now.
Final notes: I know nothing about cars; I do not know how to nor do I own the proper tools to take a battery out myself, and quite frankly the thought is pretty anxiety-inducing anyway (even jumping is stressful because I'm quite convinced I'll eventually touch the wrong thing and melt my brain). I also do not maintain the car very often or probably properly, although this is tempered by the fact that I don't drive it very often either. I tried to start it and take it for short drives every week or so over the years but I can't honestly say I've been the best with that. I think the fluids were at least checked by my friend about 10 months ago when we last replaced the battery, and were declared fit, and the car had its last professional (dealer) cleaning and maintenance and such prob < 2 years ago. I'd be surprised if I've added even 1k miles to it since then, but I can't say I've kept track.
So all that being said, I need to take care of this on my own and soon, so I just bought a self-Jump starter kit and a tire inflator that should arrive this weekend. I need to drive the car/battery over to O'Learys for testing and potential replacement, but to drive, I need to inflate the tire. But to inflate the tire, I need a working battery, since it plugs into the cigarette lighter, from what I can tell.
My question is, then: how should I go about this? Am I going to be able to read some (what I assume are not unnecessarily complicated) instructional manuals for my new tools, and then be fine self-jumping and inflating off the same, was-just-super-dead-a-few-minutes-ago battery? Or will I have problems charging the battery/providing power to the inflator (car can only idle with the flat tire)? Beyond that, is there anything else of which I need to be aware? i.e.: is the gas/oil/everything else still okay after this amount of time, etc? Is the flat tire going to return to it's "slow leak" state so I can drive on it to the battery place, or is it possibly proper-f**ked now after sitting for so long? If so, is there any way to tell beyond trying to inflate it and (I assume) seeing something going obviously and horribly wrong? AM I MAYBE GOING TO TOUCH THE WRONG THING AND MELT MY PRECIOUS, DELICIOUS BRAIN!? FOR THE LOVE OF GOD SOMEBODY PLEASE say something comforting and then tell me what to do.
Thank you in advance for any help anyone can provide. If it's okay for me to provide some more potentially interesting details about possible connections between the alarm and battery problems, let me know and I'll do so.