How can I fix my Bosch KGV2604?

Fridge compartment has stopped cooling. Although I've emptied the freezer cabinet (just in case) this compartment does seem to still be working as the temp indicator inside the freezer door reaches into the 'black' zone easily.
If I switch off the unit and leave it for a few hours, the 'motor/compressor' kicks in when it's switched back on and the temperature inside the fridge starts to fall (VERY gradually), but it doesn't stay on for much more than an hour or so. In addition, I've noticed that the fridge light no longer goes out when the door closes, but just dims.
I know it's an old unit, but I'm not in a position to replace it and as I'm reasonably adept mechanically, is there anything I can do to trace the problem and fix it?
Thank you in advance