If none of the knobs are working then the Tascam may have a hardware fault.
The Tascam will need to be disassembled and the knobs will need to be tested for continuity when turned to check if they are working ok.
Yes, a multimeter would be much easier to use for testing!
You can get one for around $20 if you don't already have one: http://www.amazon.com/INNOVA-3320-Auto-Ranging-Digital-Multimeter/dp/B000EVYGZA
If you haven't done this type of testing before then perhaps taking it to a repair store to be checked over would be best - with their trained eyes they may observe some other defects that are causing the problem.