Arctander wrote:...Gordon, the battery has been charging for a couple hours and is cool to the touch. I assume that means the issue is that it simply is not actually charging it at all - correct?
Probably, that battery is chargeable. But, prior to tasking a Roomba to charge it, you would like to know that its terminal voltage is 12Vdc, or greater.
Also, checking the PSU's voltage, as vic7767 outlined, at its pigtail-plug is a good idea, but is insufficient to prove the PSU can deliver current. A second test, using only a light bulb, will draw current from the 22Vdc source and give moderate confidence that the PSU can do work when tasked. I just connected a household type 100-watt (a.k.a., "95 watts") candelabra-based lamp across my Fast Charger's power-plug, and it drew 0.33A (and made the lamp glow). The PSU's voltage held at 22Vdc while that load was applied.
If your PSU passes voltage and current checks, the charging fault is inside Roomba, and will require repair to, or replacement of the main circuit board assembly.
If you need a picture showing the current-check arrangement, I can probably make something similar to what vic7767 did for the volt-meter check.