OTA signal doesn't work when outer conductor makes contact

Bad connectors on the coax. You really need to use the Compression fittings, not the screw on ones, for the coax. That means going from that plate all the way to the antenna and replace the ends.

Also, make sure that the center conductor of the coax to your TV is not W-A-Y too long. In the picture it kinda looks like it's longer than it needs to be... and it's impossible to tell from the picture just how much of the center conductor is already inside the jack . . .

With JUST the center conductor connected, there is probably some sort of unintended connection to the
OUTSIDE of the coax, probably due to a short in the coax or one of the connectors. With the Balun (or
antenna) in the attic disconnected, use an ohm meter to check for a short circuit between the coax center
conductor and the outer shield. To find the short, inspect each connector, looking for a stray shield wire.
And it's also possible that the antenna isn't correctly connected and the coax is acting as an antenna,
perhaps from capacitive coupling between the outer shield and the unterminated inner wire.

Those aren't twist-on fittings. They were made by Raychem (EZF connector) and were the immediate predecessor to the compression fitting. They were really popular in the '90s.

Could be a center conductor to shield short, or perhaps the cable isn't even connected to the antenna.

Then, there's also the possibility that someone hooked one screw on the antenna to the center conductor, and the other to the shield.
I've seen that one done before.

+1
I've seen that before too. 300 ohm antenna, coax cable and no balun, why just hook one side of the coax to one screw and the center conductor to the other

I forgot all about those.

They were worth forgetting about...

I remember when we tried to put two of those baluns back-to-back, to make a "shield breaker" for the return-patch signal we were sending to TCI Cable (yeah, it was a few years ago).
We could not get rid of the hum....no way!
Took them apart, and found that the local parts house had bought a whole slew of "look-alike" baluns. One wire went to the shield of the coax, the other went to the center pin.
No telling how many were sold across the country.

Those make things so much fun! Glad you found the culprit.

I think I've made that inspect for stray wire recommendation dozens of time.....
But you're perhaps the FIRST to actually admit they found it....congrats.....
No one else seems to want to talk about it.....

That is all it takes. As for the Stinger, I usually only leave about a 1/8", or the thickness at most of Quarter sticking out. That way, the stinger goes in first, then you turn the connector counter-clockwise to get it to sit, so it is not cross-threaded, then tighten clockwise until tight.

I picked up one of those radio magazines last night, and the author was saying he gets more channels with the transformer removed, and the balanced feed wired to the unbalanced coax.
I wonder if he has a short in his cable, too.

I wish I had a dollar every time I found one of those.

BTW, those Raychem fittings weren't that bad except for the RG59's with the barrel falling back from the center when disconnected.

Good job finding the issue>