Doesn't matter what channel is used, there are always running diagonal lines in the RF output of one VCR. It seems to be isolated to this VCR and not the cables. What could be causing them?

A picture and/or fuller description would help - how many are there, do they run over the full picture height, do they vary in intensity, etc. etc.?

Good point. A picture would be difficult to get, but they're subtle diagonal stripes (a shade lighter or darker) that move towards the top right (diagonal) moving quicker and quicker until they move so quickly that they disappear.

They eventually slow down and appear still, then reverse and repeat the process the other direction (towards the bottom left) then slow down, stop, reverse, and repeat.

It's most noticeable with red.

My guess would be the power supply on the VCR.

Seems like a reasonable guess. Do you know if the stripes also are in the composite video output?

Nope, only on the RF out.

Is there a way to repair the power supply, or is it dying?

Stripes only on the RF output does not sound like a failing power supply. Maybe RF interference from the power supply or some other VCR or piece of gear.

Time to do a process of elimination. Swap out the output cable(s) for another one(s) to check for bad shielding/grounds. Unplug other gear one by one to see if the interference goes away. (Don't just turn them off, as the power supplies may still be running in standby mode.)

I have seen that with some of my Betamax machines. Changing the RF cable usually helps. On some of them, it is not possible to eliminate them. On those I use a RF modulator.

Sometimes one or more RF switching diodes or transistors that pass signal from the ANT-IN to the VCR tuner and select between Antenna and the VCR's 3-4 modulator when playing or recording, get zapped from a nearby lightning strike or somesuch. That can cause diagonal lines in the RF 3-4 output.

Look in the RF modulator for 1uf and .47uf electrolytic caps. They were notorious for failing and causing that.

Time to do a process of elimination. Swap out the output cable(s) for another one(s) to check for bad shielding/grounds. Unplug other gear one by one to see if the interference goes away. (Don't just turn them off, as the power supplies may still be running in standby mode.)

Just did this. Tried unplugging everything that wasn't the VCR, source, or TV. Lines remain.

Tried changing the cable. Lines remain.

Tried putting in an RF modulator instead of the VCR. Picture quality is awful, even by RF standards, but the lines are gone.

Look in the RF modulator for 1uf and .47uf electrolytic caps. They were notorious for failing and causing that.

I'll give this a shot.

Sometimes one or more RF switching diodes or transistors that pass signal from the ANT-IN to the VCR tuner and select between Antenna and the VCR's 3-4 modulator when playing or recording, get zapped from a nearby lightning strike or somesuch. That can cause diagonal lines in the RF 3-4 output. If all else fails I would think this would be the path to pursue.

Look in the RF modulator for 1uf and .47uf electrolytic caps. They were notorious for failing and causing that.
+1 for this, caps can cause all kinds of weird problems I wouldn't think to attribute to them initially.