This is an old post, preserved for reference.
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A common cause of a black screen*, garbage on the screen, intermittent startup or general instability in Commodore 64's is the 906114-01 PLA chip. A custom gate array chip which handles all the address decoding in the C64. As usual, original stocks dried up many years ago, but there are various options to replace these. It is sometimes a bit of a lottery, as the timing in the C64 was never quite right. You can get a C64 that will only work with some PLAs, or PLAs that will only work in certain C64s.
C64 EPROM PLA replacements). It sort of works, but with mixed results, better on some boards than others.
this video shows you can get a similar effect by adding some additional capacitance to the pin.
diagnostics cartridge and test harness and with an assortment of games it seems to run well,
* N.B. when I say black screen, this is video sync but only a black screen displayed. This is different from no video sync, which usually indicates the VIC II chip is at fault.