Having successfully fixed my TDS1002B yesterday (for the third time) I thought I'd put a post out in case anyone finds the same problem.
My scope came to me with a fault where it wouldn't start up. The back light and LEDs would flash every second or so but it wouldn't get any further. I guessed that it was a power supply issue and investigated more. I believe it's got a flyback producing around 12V and then several other supplies off that one. The power rail would go too high, hit some sort of over-voltage threshold and then turn off. And repeat.
I spent a while desoldering, testing and replacing a load of components in the feedback circuit without finding any iffy parts. As you do, I plugged it back in and it worked! Aha, iffy solder joint!
It's failed twice more since then. The second failure was exactly the same but now I knew what I was looking for so I just hit a load of joints in the feedback circuit with the soldering iron until it worked again (I know - scientific right?).
The third failure, I was really struggling. Hitting all the solder joints in the feedback circuit with the iron did nothing. Eventually I found a tinned wire link that clearly had a bit of extra oxygen etc. No solder was sticking to it. I replaced the wire and problem solved.
When the scope came to me it had clearly had a rough life (some impressive laser burns). It's possible that the solder just cracked from physical abuse. Since then, it's had a fairly gentle life on the shelf as I tend to favour my Rigol so I don't know why it's kept failing.