A few obvious things to check/try.
1. Carefully attempt to remove all the dust from the system. Be careful with vacuum cleaners generating static though.
2. Re-seat all the connectors and RAM. Again, make sure you're properly earthed to the case before handling components.
3. Check the power supplies - eventually the big capacitors dry out and system regulation goes unreliable.
4. Also check the motherboards for vented capacitors - many of them have a scored lid so that if internal pressure builds up they vent through a known weakness rather than just explode.
5. Make sure all the fans are rotating cleanly and at a sensible speed. You can get programs to monitor fan speed and system temperatures.
I always keep a spare power supply and selection of fans on hand because they're the items that fail the most. If it's been a bit warm or you've had a sudden surge of dust due to another cause, it's possible that two machines might have gone close together.