It is possible, not likely that the Pronto's don't use WiFi.
Any TUS9400's that are using WiFi will probably have a little indicator in the upper right corner of the screen. It resembles an antenna. If this is replaced by a question mark, the unit is attempting to connect to WiFi.
Purchasing a unit online may not solve your problem because you will not be able to extract a program from the TSU9400's. Hopefully, the customer has a copy of the program.
In the server room, look for some Philips "boxes". These will likely be 1U rack units (wired to the network), but there is a smaller (plastic) unit that may or may not be wired to the network. These boxes may be scattered about, particularly the smaller unit.
If all of the IR emitters are really wired back to the central room, it is possible that the 9400's are strictly IR. If this is the case, there should be an IR receiver near each TV. However, I don't think that many of us would design a system like this. If you can't find any "boxes" the system is strictly IR.
By the way, most (not all) phone cameras will respond to IR. Check one of the working Pronto's to see if it is emitting IR commands. You'll need to check bunch of buttons for different devices because the unit might be programmed to use a mixture of IR and RF commands (on the same button).
Also, if the WiFi password has been changed, the Pronto commands that use WiFi will be locked out.
