Hi John, I'm not sure which model you have, but this is one of the early ones from what I've been told. The Owner's Manual has a stamp from Arachnid dated 1982. It doesn't even have cricket on it, which is kind of a bummer, but it's fun just the same.
We've tried both of your ideas, to no avail. We've had the membranes off several times and even managed to get it to work for about 5 or six darts, registering properly, and then - bang, it stopped scoring again. I repeated the same method two more times to no avail. I'm thinking this is probably the reason the guy I got it from got it so cheap. He was told it was a basket case and bought it for spare parts, got it home fiddled with it, and it worked fine, so he offered it to me at a very decent price.
I'm trying to avoid buying a new scoring matrix if I can, but it's looking like I may have to. I have all the documentation for this board if anyone is looking, by the way. I know the Owner's Manual is available on line, but I also have all the schematics.