I agree with Wallace.
If its working over 4V, the power transistors are OK. You can clean them, but it will only be cosmetic.
I have fixed dozens of such linear PSU. Most often, the power transistor are OK. When they are fried, there is no output.
Most often also, the big capacitors that filter the input line are OK, or do not affect the functioning of the unit.
The problems comes with the small electrolytics capacitors associated to the opamps that cannot then regulate properly the output. In some cases the opamp could be damaged. But
first verify the capacitors.
For units that stayed for a long time on the shelf the potentiometers can pose problem. In some cases ,just turning them a few time fully CW, CCW will fix the problem.
There may also be a pot on the board that can be adjusted to change the minimal voltage of the unit. There seems to be at least one in your pictures.