I bet one of the integrated circuits is bad.

Check the output of the voltage regulators and make sure it's in spec (one is -5 VDC and the other could be +5 VDC). Desolder the caps (at least one lead) so you can measure their capacitance with a multimeter while they are disconnected from the rest of the circuit, and see if any have gone out of range. The cheaper ones will dry out with no visible change so the only way to know whether they are still good is to measure them. The device looks pretty simple so if all that ends up ok then you may have a broken IC, but that's pretty rare unless it has been subjected to static electricity damage.

If you have an oscilloscope you can measure the voltage going into the ICs to see if it has any significant ripple on it. If it does, then it's almost certainly down to bad caps. I recently got a Behringer SRC2496 sample rate converter working again due to this. The multimeter said the voltage was spot on, all the unit's LEDs worked but the front panel buttons did nothing. The oscilloscope showed bad ripple due to failing filter caps, so I replaced the caps, the ripple went away and the unit started working again. Essentially the voltage was going up and down so much that the unit's processor was being reset 100 times a second, so it could never boot up to the point where it could respond to button presses.