Hi,
at first I would try a visual inspection, normally the Caps are visually damaged.
Charging the caps (any battery does the job, you don't have to use the Ohm-Range) and discharging them via the input-impedance of your DMM would do, then you have to calculate your time-constant (tau=RC) and so on... They have to be desoldered first!
Faulty caps normally have a big difference in Capacity (nF instead of µF), so this method may be accurate enough, but this is kinda annoying. Maybe it's time for a new DMM, even the cheaper ones have a C-Measurement build in.
Another type of diagnostic is the ESR, I'm not sure if the new DMMs can measure this (mine can't).