So…any luck?
Is there a switch on the VCR to tell it whether to spit the signal out the coax or the video connector? Can you hook the coax up to another TV temporarily just to verify that a signal is actually being generated?
No, that doesn’t work.
Because it was cheap and I was broke. And the switches are all right, else I couldn’t receive a normal broadcast signal.
No. 
I’m going to try galt’s suggestion next - the different TV part, not the switch part. I just wonder if it’s not the VCR.
Don’t know if this has anything to do with it, but on the last page of the online manual it says that the TV is 240V 50Hz (UK voltage I guess). The US is 110V 60Hz. Are you using an AC voltage converter?
Yep, no issues there.
What really bothers me is that I never had problems like this before - it was all pretty cut and dried. Plug everything in, turn it on, tune the TV, and the VCR channel was automatically tuned in.
Are you sure the problem is with the TV, not the VCR? What happens when you plug the VCR into a different TV, what channel does it come up on?
That site is sick! Sick! The cathode ray tube by virtue of both programs it displays and by its warm, glowing warming glow, is a great source of spiritual and mental nourishment. Why do you think it’s called the Glass Teat and the Boob Tube?