You can test the panels with a good multimeter that has a clamp-on current
meter. Disconnect the panels from everything so that all you have are the leads from one panel (or the terminal blocks on the panel if that is how they are configured). Put your multimeter on DC Volts and read the voltage (in full sun) across the terminals. This will give you the open circuit voltage. If these are 36-cell panels (most likely for 85W, but could be elsewise) you should see something in the 20-22V range.
Cover the panel with something so that it has no light (none!). Short the wires together, then put your clamp-on ammeter on the shorted leads. Remove the cover so that the panel is in full sun. Measure the current
. Again, if they are 36-cell panels you should probably have something like 5A. Re-cover the panel to re-connect the panel.
That's the easy testing, can tell you pretty quickly if the panels have basic function. After that you have to put an actual load on the panels to see if they actually put out power. You could connect them direct to the battery
(bypass the controller) if you have a way to measure current. If they charge at a higher current that way then either a) the controller is the problem or b) the batteries are fully charged (or the controller thinks so). A short test like this should not be a problem for the batteries.
Is there a diode between the controller and the batteries? That can cause 0.5-1.5V drop and fool the controller.
Lastly, if your panels have bypass diodes that are not protected from reverse polarity (at they age they likely weren't), and were ever connected reverse polarity without a fuse in the line then the diodes could be damaged and you won't get much out of them (a study of small village power systems in Thailand
found 18 out of 31 systems were not working after installation
because of this one problem Bypass Diode Failure