I think the 613SS4 max is 20 Volts, and if the Tantalum capacitor is rated 24 Volts, usually the circuit is run way under the maximum in order to have a safety margin. I would guess your encoder board is meant to run with 12 Volts.
The 7i37 looks like it will take up to 24 Volts. You should check with Peter (from Mesa) to make sure but I think the inputs are just like a 4.4k Ohm resistor and an LED in series. Sorta like this:
(Click on image for lager version)
You need two wires for each encoder output. One to supply the signal, another to complete the circuit to the encoder board's ground.
I would think that you could do a lot of testing before ordering parts. It may be the burnt capacitor is the only bad part. I'll need to do a little more research to find an equivalent for the 613SS4.
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Kirk Wallace
www.wallacecompany.com/machine_shop/
www.wallacecompany.com/E45/index.html
California, USA