Good news! By "button" do you mean the light, or the input (i.e. do the yellow doors open and close when you press it)? If light, it'll just need a new bulb (Bob probably has whatever bulb it uses - I've never opened up mine so I don't know what bulb is used). If input, it may need a new micro switch (again, available from Bob) or it may also be that the switch has popped out of place and just needs to be popped back in. Whatever the exact problem, you're down to "simple" stuff so I'm sure you're excited about the progress.
As for the screen, do you mean the image is rotated by several degrees (as opposed to the monitor somehow physically sitting in there wrong)? If so, your problem will be the yoke on the neck of the tube. That's the big ring with all the wire windings on it. There is a screw to keep the yoke locked in place which may be loose. Loosen it if needed, then carefully rotate the yoke, but avoid shifting the yoke forward or backward on the neck. Otherwise you'll end up with picture problems (red, green, blue don't converge to form a tightly focused dot as well as possible color purity (splotchy) problems). Also be careful to keep those rubber "bumpers" in place. They should be glued to the tube but sometimes they come loose. They help keep the yoke aligned properly. Then tighten the screw back up but obviously be careful not to over tighten.
Whether or not you get a spare power supply boils down to how much you want to learn to work on arcade games. Power supplies, particularly the MT supply, are pretty simple to repair if faulty. Personally I'd rather repair what I've got in there if it ever fails, but to each his own. Nothing wrong with throwing a switcher in there if that's what you want.
P.S. Would you mind rewarding those of us who have offered advice with some pictures of your game? I'd love to see it.