Regardless of your parental or financial situation, you can in the least, have a pro or 2 or 3 estimate the cost of the repair(s). I don't think anyone on this Forum can properly evaluate your situation. Even if I/we knew the make/model/serial-# of your 'switch', whose to say that's what is wrong? I'm sure if you knew what was, EXACTLY, wrong, you would have had it fixed already.
Fortunately, the estimate won't cost you. IF you can find out the problem and perhaps if you know an electrician (or maybe a friend knows one), maybe for a reasonable amount of $$$, 'they' can fix it. From the tone of your Post, I wouldn't suggest you do the fix EVEN if it's JUST the switch especially where there's fuel and electricity present. Get someone to evaluate the problem and tell you what's wrong. From there, get the make/model/serial-# of your OIL Furnace (not the switch), and see if you can start 'networking around' to get any new/replacement parts installed from a friend, or a friend of a friend.
As an aside, try and stay away from taking $$$ from your 401K unless you absolutely, POSITIVELY have to. Once you 'dip' into that, it's too easy to do it again. (Besides, you may have to withdrawl out MORE than you need, as a minimum! 1) You pay a penalty on that $$$, 2) you pay taxes on that $$$, and 3) you can spend the 'excess' $$$ that you withdrew on 'stuff' that you normally wouldn't have bought.) I'd consider borrowing from a family member or friend, your employer, home equity, or getting a 2nd job on the side (IF you can swing it with your 12 yearold, but maybe not.) Or, see if Monica will use her babysitting $$$ to pay the bill until you can pay her back. 'Nough said.