This is a Galaxy 30. Yes, the valve is broken. Worse, I find out the valve is no longer available. So here goes–you can make the currently available valve work.
First, you have to have a method of testing the toilet. I have a couple of fittings that allow me to hook it up to a hose.
Second, you order the valve and look at the differences. The mount, operation, and connection to water are the same. But the water goes out a different direction and there is no hook on the new valve for the water-only foot pedal.
Third, take the whole mechanism out of the toilet by removing 5 screws.
Note the path of the hose and where the new hose needs to go. Then cut a new hole and shorten the hose to fit the new valve. Hook the spring onto the end of the big spring and put it all back together.
The new hole could have been a little bit closer to the old hole and a bit to the right, but this works. BTW, you can order a new two-pedal mechanism for $120 (but why would you if a new Style II is available for $180?).