On the 125, there two safety interlocks, and either one will cause the starter interrupt, i.e., nothing will happen when you turn the key, the starter will not turn over. One, the PTO must be disengaged, and two, the clutch/brake pedal must be depressed. If you can get the starter to turn the engine, then the safety switches are ok. There are no other special safety features on a hydro over a gear drive on the older Cadets.
If you are cranking and there's no spark, and especially if it has sat for a long time, the points are corroded and not opening. Take the points cover off (left side of engine, front, bottom, little cover protruding out about 1" x 1" x 2"). Crank the engine and see if you have a nice blue spark at the points. If not, a little sand paper will clean them up.
Getting the tractor to roll freely may be difficult. There is a Hydro Dump lever on the side of the transmission tunnel, right side of the frame. This must be held up while pushing the tractor. If you lift this and there is no resistance, the arms are broken off (VERY COMMON) and you cannot roll the tractor. There is no other disconnect for the hydro on a 125. Later hydro cadets had self dumping transmissions, so they would roll around when turned off. This one does not, so the hydro is always locked. Even with the dump lever held up, if it's working properly, it will NOT roll like in neutral. There is always some drag on the hydro, so it will whine a little and be a little difficult to push around.
Honestly, if it ran when parked, the easiest way to get it going will be to put a new spark plug, new points, and fresh gas in it. Completely drain the tank and put new gas in it. Tap the float bowl on the carb a few times to get the float unstuck. Also, Sea Foam makes a product called Deep Creep. I would take the fuel line off the carb and spray this into the carb fuel inlet. I would also spray this into the air intake of the carb and the spark plug hole while the plug is out. Spray a ton of it in and just let it sit for an hour or two while working on other things. This stuff works miracles on old engines that have sat for a while. Trust me!
Bill