Electricals are my downfall

In addition to the problem with my four-way Z-Wave switches, I have also been unable to use the lights over part of our kitchen counters for months. It took a long time just to get the bulbs replaced, figure out that wasn't the problem, and conclude it must be the ballast, and then try to figure out how to open the unit up and give up for fear of breaking something. The electrician showed me what screws to undo -- as you'd expect it's terribly easy, but if you don't know, and you undo the wrong thing, who knows what'll come apart you can't put back together. Another couple of months before I could bring it to Home Depot to look for a matching ballast, which I did yesterday, only to find out they don't have them. Next stop is those small local electrical supply shops that are supposed to have more personalized service, but actually just tend to make me feel condescended to and unhelped because of not knowing enough to follow the jargon or ask the right questions.

I did manage to find a replacement bulb for my motion-sensor floodlight. However, I've just swapped it out, and nothing. I can't find an owner's manual for the floodlight, but it doesn't look like there's anything particular I could be doing wrong, or not doing. One of the contacts looks a little corroded but not badly, not enough to completely impede all functionality; I tried scrubbing it a bit, but it didn't help. Once again, I'm at a basic dead end on something that is probably a very simple issue.

Of course the floodlight itself is not a big deal -- I could buy a new one for $25, but could I install it, or would I need an electrician to wire it in at a cost that makes the fixture itself seem like nothing? I can't even be sure that the fixture is the problem. Maybe it's the motion sensor. Maybe I'm putting the bulb in wrong. How frustrating. My multimeter shows no voltage across the contacts.