Its wise to point out we need to do some tests first before we blame the A600.
1. what video output source are you using?
RF, Composite or RGB Scart?
2. Have you tried another output source?
3. Have you tried another monitor?
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If the answers are yes to all these questions, then we can continue
1. Possibly the video feed capacitors VIO and VOUT are failing - is on its way out - I would say replace
C459 ( 0.22UF ) capacitor.
C460 ( 10UF ) capacitor.
C408 ( 1,000UF ) capacitor.
C409 (100UF) capacitor.
ensure that you get the same voltage values or slightly higher - thats to say you can replace a 16v with 25 volt and it would be fine.
2. Final 4bit of each RGB component is produced by U31 and U32 respectively, both of these IC's are 74HCT244, both are also SMD, you can get these from various places for very little pennies, I may even have some spare, but to replace them you will need to use hot-air (or have ninja soldering Iron skills)
I seriously doubt that either of the logic IC's have developed fault, I suspect a video power feed in all honestly
Anyway, that would be my suggestion, I do hope that lot helps