Motorcycle turns but won't start

I have a Suzuki Bandit 1250s. It was standing for about a year, after which I decided to ride it again. But it started giving a problem where it won’t start when hot. The engine will turn like it has a flat battery, but when you leave it to cool down, it starts fine. That went on for a week or two, but now it won’t start at all. I got it a new battery, but still it won’t start. The battery is reading 12.7V, but the bike is behaving exactly the same way as with a flat battery. The engine turns a little, but sounds like it does not get enough power. Sometimes, a chance one in 50, it will start with great trouble.

I am able to push start the bike with ease and the bike runs fine after push starting it. I gave it new sparkplugs, air filter, oil, coolant, checked connections, all the fuses are fine.

It does not sound like a bad starter motor to me, not sure if it might be the brushes? I don’t have allot of experience with fixing bikes, so not sure if that might be a possibility. I also bought it with an aftermarket alarm/immobilizer system, but as far as I know that will prevent the bike from even turning the engine.

Any ideas on what could cause a bike to behave this way? Any help will be appreciated.