I took out the old capacitor and didn't remember to check the polarity because I assumed the board would have more standard markings. Is there any way to figure it out with a meter or by the printing?
The pin on the left is connected to the large power plane, the next task is to figure out if it's positive or negative with respect to the other pin, since the HC125 is connected to it, it would be the ground plane, but if the board has multiple voltages, you may have dig a bit more. If the right pin is connected to pin 14 of the HC125 then it would be positive wrt the ground plane connection.
You cannot identify this from the board printing.
However you could look up the pin-out of the 74HC125AN and use a continuity testor on the powered-off board to figure out if either lead of the capacitor is connected to its ground or supply. Or to a labeled ground connection elsewhere on the board.
Continuity testors must only be used on unpowered systems, and unpowered means not only having no supply connected, but also not having any high voltage capacitors which retain charge (especially in legacy TVs, camera flash units, etc). That's probably not the case here but still needs to be said. Also using a continuity testor is not 100% safe - in theory the injected current can damage sensitive circuits but that is also relatively unlikely here.
You may also be able to trace connections to known power/ground pins by eye.