My 1974 ironhead was running fine, then I parked it. The next day it wouldn't start with the push button ignition. I got it started that day by push starting it, but after that, it hasn't run since. I replaced the battery, wires and plugs, but still nothing. It will turn over, but it just won't start. Could it maybe be a faulty generator? Not sure what to do from here. Any help would be great, thanks.

 

The generator has nothing to do with starting. I'd clean the carburetor, put fresh gas in it, and check/service the points.

 

Don't think gen. As long as the battery is up it would start and run with no gen.
Best suggestion I have is to follow the FASTTEC method.
F uel A ir S park T iming (ign) T iming (crank/cam) E xhaust C ompression
Go to Youtube for a in depth tutorial but a quick discription is;
F uel - pull a plug, hold a piece of paper in front of the hole and crank it over a few times. You should see a wet spot that smells like gas on the paper. If not; low fuel, fuel shut off, plugged filter,
A ir - not likely but if it doesn't try to blow the paper away while you are cranking it something is up. On cars people have stuffed rags in the inlet while working on them and forgot to remove them.
S park - While you have the plug out take an old plug and open the gap up to 1/8 in. plug it in the wire and hold the threads on a ground and crank it over,you should see a spark jump that gap. If not don't just start changing parts. Test
do you have 12v to the coil WHILE CRANKING? Do you have juice at the points (when they are open)? I had a bad battery ground connection once, It would still crank over fine but the starter was taking all the juice and there wasn't enough left to fire the coil reliably. But this isn't something that happens over night. In your case if there is no or weak spark and everything else looks ok I would replace the condenser. That is about the only part that would fail with no warning. It is very rare, I had it happen once about 45 years ago.
But really, watch Matt's you tube video, and take your time and test before you start changing parts, You could have hooked up jumper cables to a car, if it still didn't start you probably didn't need to buy a battery.