So, I've worked on a couple of these, and they have a few failure points/common problems from what I've seen. Couple of questions, though:
- Does the green LED power on?
- You hear it energizing - is there neck glow?
If it sounds like it's powering up, that's a good sign. Unfortunately, you'll need something to drive the display, as they can be uncooperative with nothing to draw. The dials not appearing to do anything is normal in your circumstances, especially for how long it's been sitting. If you have it disassembled, adjust the screen pot on the flyback (should be the bottom pot on a narrow slit on the flyback enclosure) back and forth to see if you can get a raster to appear on-screen. If the screen gets bright, then it's "working". At that point, you're going to want to recap it; you're going to want to do that anyway, but this will at least confirm that the electronics are operational-ish. I'll include the Mouser project lists with the caps below. I made these lists a couple years ago, so some of the parts are almost certainly backordered or out of stock but there are alternatives available. If you can get a raster of any kind, play with the sub-brightness and sub-contrast pots on the top of the neckboard to see if you can dial in the raster and focus (too great a contrast will knock focus out of spec). Once you have it relatively dialed in, the dials on the side that are normally what you would use should give you some kind of response when turning them now. If it seems like you're having to waaay overdrive everything, then the monitor is almost certainly good and just needs to be recapped.
You will also want to inspect a large green resistor (I can't recall the value off the top of my head) near the front of the chassis near the tube. It may either have no signs of wear, have heat damage in the vicinity, or be completely burnt out and destroyed. This is part of the power regulation circuit and has a decently high failure rate due to cooking itself to death after prolonged use. If it looks fine, test it to make sure it's within spec and then forget about it.
Apple M1296 12" RGB Monitor - Neck
Apple M1296 12" RGB Monitor - Chassis