Sid is the audio chip. In Fact the c64 will work fine if you take the sid chip out, just no pad, mouse, or sound operation. Try going through these steps.
UA4 THRU UA7 & UB4 THRU UB7 8 RAM CHIPS (4164) on CPU board.
Blank screen, no border. Shorted chips will get warmer than the
other RAM chips. Partial failure can produce screen or program "freeze"
or "garbage" screen. An abnormal (less than 38,911) number of bytes free
or "out of memory" error on startup screen is a RAM problem.
UB2 906108-02 (6526) CIA on I/O board.
Startup screen normal, but no serial or user port access. "File not
found" error when drive accessed. Cartridge works. Partial failure:
characters may show as blocks on startup screen or screen will fill
with lines inside border.
UB3 906108-02 (6526) CIA on I/O board.
Startup screen normal, but no cursor. No keyboard or joyport
access. Partial failure: some keys or joystick positions don't work.
Cartridge works.
UC1 CD4066 QUAD "SWITCH" IC on I/O board.
Proportional mouse or graphics tablet doesn't work. Check also
SID chip UE3 on CPU board.
UD1 901225-01 CHARACTER ROM on CPU board.
Blank screen w/ border. "Garbage" characters where startup page
info should be. Cartridge works.
UD2 7406 LOGIC on I/O board.
No (or intermittant) serial (drive or printer) access.
UD3 251104-01 KERNAL ROM on CPU board.
Blank screen, no border. Cartridge works.
UD4 901226-01 BASIC ROM on CPU board.
Blank screen with border. Cartridge works.
UD7 906107-01 (6510) MPU on CPU board.
Blank screen, no border. Cartridge doesn't work.
:huh: