As far as that Marquee light, I have had two of them lately with a Bad Ballast. Not the starter, the ballast.
First, replace the starter. if that fails, take out the blub and put it back in. If it still doesn't light, check to see that you have 110v at the AC IN. Usually the marquees have a molex connector of some sort. Probe that.
If you have 110v, a new starter, replace the ##@!@ bulb. If it still won't light, check the connections at the edge. One of the ones I replaced the ballast also had a real flaky connection to the light connector. It was loose on the inside. It had a retaining screw that must have worn down and the wires frayed over the last 23 years.
I did all that, and nothing. I had a couple of ballasts laying around and I put it in line. Bink. Light comes on. Ballast was bad.
Most of the time a starter fixes it. If that doesn't work 9 out of 10 times the bulb is bad. But lately 2 with bad ballasts. Both midways. One in a Wizard of Wor and the other in a MsPac.