Did you ever get this fixed? Although I believe the PCBs are a lot different AFAIK Hang on still uses 2x 68K CPUs as per (turbo)Outrun and I have just chanced on the following repair log that might help:
http://www.arcadecomponents.com/repairlogs.html#66687
"
Sega Turbo Outrun is missing obstacles and
backgrounds
This was a strange one. The sky and road obstacles were
missing. The buildings were there but the road and the car never moved
left or right. This was a problem with the subprocessor. Built-in tests
showed one of the ROMs bad. ROM read good in an EPROM programmer and a
replacement ROM gave the same symptoms. Checked all the pins on the
socket for continuity. The ROM pairs (High & Low) had a common CE
line. This was driven by a 74LS138. The chip had badly rusted legs.
Replaced the chip and the game worked normally. The rust had travelled
up the body of the chip."