I found your message a little late :)
Have you been able to revive your 4051 yet?
My 4054 had the exact same symptom, I found that one of the socketed DRAMs was bad and
I do happen to have the two volume service manuals for the 4051 I used in the 70's.
The CPU Board has all the 6800 components and the two banks of 4K bit MCM6605L DRAMs for
8K Bytes of standard DRAM.
If you have the memory expansion board - options 20 (16KB more), 21 (24KB more) or 22
(32KB more), you might try unplugging that option
card to see if the 8KB base memory is ok.
If yes, then try unplugging banks of option memory to isolate the bad DRAM(s).
The troubleshooting guide says check the 6800 section first if the unit fails to power
Contact me directly for more info.
4052 and 4054 owner