It would be helpful to know what problem you are having with it
Get the schematics. Understand the schematics in terms of functional blocks. Try to locate a suspect block based on the type of failure you are experiencing. Are all of the chips seeing the correct supply voltages? Any getting hotter than the others? If there are socketed chips and you can swap some around, try that and see if the problem moves with the chip or changes in some way. Get an EPROM burner/IC tester and test all of the socketed stuff. If you don't have an oscilloscope, now is the time to get one.
I wouldn't remove soldered chips unless you have a good desoldering tool and are confident of doing the the work without doing more harm than good. If you have found the defective chip and have only basic tools, then go ahead and remove it and repair any damage done. If you know it's the bad chip and can sacrifice it, cut the legs off first; it'll make desoldering easier and lower the chances of lifting a pad or trace. Use a nice machined pin socket.
If I'm looking at something without a schematic or much of a clue, here's what I do:
Look for a mechanical fault (90% of all "electronics" failures). Bad ribbon connectors, dirty contacts, broken pots/switches, etc. Check for cold solder joints. You can learn alot about a circuit while running your eyes over it looking at the solder joints.
80's stuff with a battery? Check it! It may be pulling down the logic supply if it's dead. It may have leaked and taken out nearby components or a trace. Sometimes factory settings need to be reloaded after a new battery is installed before the unit will wake up.
Swap boards around. Swap components around.
Check IC pins. Power? Look for floating inputs. Look for outputs that are not at logic levels. Check the bypass caps, they tend to fail from power cycling, and they can fail by shorting.
Check that the microprocessor is in a good state (initial conditions met) and has a good clock.
There are many things that you can learn about a circuit without much of a clue or any documentation, but since the service manual is available you don't need to bang your head on the wall too hard
Good luck, I hope get that nice synth running!