I haven't been using my 2235 in years, since I got their new TDS3032B. (So I'm short on remembering which switches to flip fo quick checks).
Have you got an operator manual for it, or can you check on-line for it?
People here highly recommend websites with Tektronix forums for information that will probably be more explicit.
You may have a circuit problem, but I ALWAYS try the simple things first. A lot of times problems tend to be with switch configuration, and not actual circuit failures.
Before you tear into the scope looking for the trouble, I highly recommend playing with the controls to see if something simple is holding-off your sweep.
I realize you've already tried that, but I'd look over the operator manual just in case you've discounted a possible check that should be done. I can't count how many
times I've made simple mistakes when troubleshooting instruments, only to find out I had the control panel incorrectly configured.
If you don't get a reply here that can give you specific ideas, I'd Google the Tektronix discussion forums and ask the guys who work with Tek scopes on a daily basis.
Good luck, and I hope it's a simple fix, and not an expensive repair.