The phrase you are looking for is:
"You hired an IT professional for a reason. You can either let him run the IT or you can second-guess him and block every move."
Have used it. It becomes a self-fulfilling prophecy. Either they take it on board and admire your spirit, or they ignore you in which case they would have ALWAYS ignored you. At least then you can walk in the first few days of the job rather than clinging on for four months.
There's a certain bell curve of how suspicious things look to a future employer depending on the amount of time you were at the previous. 4-6 months is the peak of the curve. If you only last that long, there was probably something wrong with *you*. If you walk early, or work there years, there was probably something wrong with *them*.
And, sorry, but "rebuilding" the 2000 machine by poke-and-retry, and having to source original hardware at great expense? I judge *you* for that. Has their situation improved for all the work you did on that? No. Do you have backups of that stuff still? When it next goes, are they going to hope they can find another identical model of computer? Did they ever get a lightning rod? You improved nothing.
The proposal was your saving grace and when that's rejected, yes, you walk.
It's hard walking into an established place and making changes but it's do-or-die. I have done this at several schools (I work in school IT) and on more than one occasion told them they just need to wipe everything and start again. It was that bad. I got it working whenever I was allowed free reign, on the same hardware, no further cost, by doing things properly. In one case this meant everything down to the network switches, which were purchased as and when and used like mains extension leads to "double" connections, join in new offices to old cabinets etc. In several cases, I made an explicit "I stake my reputation that that's the problem and that it will improve if I can replace this and this" calls to my direct bosses.
In one case, where an IT consultant had covered the period until they could hire me, I even had to go so far as a: "*I* will *personally* rebuild all those systems, but I'm *requiring* that he get the f*** out of the way and not touch a thing. If I'm right, they will work as I've been promising all along. If he gets in the way or tries to help, I need him removed. If I'm wrong, you can have my cards ready. If I'm right, please get rid of him" call. Guess what, I was still there.
It's a tough call but everyone is so precious about their jobs that they never want to make such ultimatums. You have to think to yourself, though, what have they hired you for if not to fix their IT, and if they don't listen what are you left with? Known broken IT that you can't fix and which you'll take responsibility for. What the hell kind of job is that to be in? Get out of there fast.