I got my hands on a faulty TDS220 recently, which I managed to repair, and thought I'd share a report on what was wrong, in case it's of any use to someone else out there.
There was no probe comp signal present. Power rails were good. Main clock, CPU clock and display clocks were present, there was data flowing to/from RAM, but none flowing to/from the CPU or ROM.
Probing around, I noticed the 68000 would go into halt 10µs after /RESET went high. I presumed it was fetching invalid data from ROM, throwing an exception, then throwing another exception when trying to handle the first exception, which caused it to finally halt. I'm not sure this is what the 68k does, as the manual isn't terribly specific about what causes it to assert /HALT - in any case, that's the hypothesis I went with.
The main board is a newer revision and has a BGA EEPROM chip. Reflowing the EEPROM seemingly brought the board back to life; however, there was still nothing on the display, despite there being data flowing on the display data lines.
I noticed the -24V line going to the display was dead, even though the -24V line from the power supply was good. I couldn't be arsed to figure out the circuit for the LCD -24V line

so I just bodged it straight to the -24V line coming from the PSU.
That made some stuff show up on the screen, as seen here:
I reckoned there was something wrong with the display - and indeed there was: a faulty electrolytic cap. After replacing it, the scope came back to life, as shown in the attached picture.

I'll see about replacing the display polarizer, as it's in a sorry shape. Yes, the display is inverted - lowering the contrast makes the colors the right way around, but the middle area becomes almost unreadable, due to the bad polarizer.