2010 crf250r wont cold start

Verify proper valve clearance. Not starting cold but then starting hot is first symptom of loss of valve clearance.

It also could be a bad coolant temp sensor. If the sensor is faulty it won't report to the ECU to richen the mixture for cold starting.

Sounds like a sensor problem. Because of incorrect sensor feedback, its not delivering the correct amount of fuel while cold. Coolent temp sensor is where id start.

So this is going to be long winded, apologize in advance.

First thing to do is check valve clearance, if you can can do a leak down test that would tell you a lot. (Which not easy on these engines without a way to nicely hold the crank in place)... Even with correct valve clearance you can still have excessive compression loss if the either of the 2 exhaust or 2 intake valves are leaking. Occasionally, if the intake seats are leaking bad enough you can sometimes hear the compression stroke combust fuel/air and it will sort of spit back up the intake track. Another thing, you mentioned the engine seized.... I don't know the extent of the engine failure but I can tell you that the cam gear can slip on the camshaft when the engine locks up if all the perfect scenarios happen, thus retarding the valve timing which can SIGNIFICANTLY impact starting ability. The loss of compression from this as well as the decompression lever timing moving has a role in this. I have rebuilt multiple nasty engine failures and when I check the valve timing it has moved significantly (retarded). Is it likely yours did that? Probably not... As for the fuel injector not spraying fuel that's more concerning. You can back flow the injector with some tubing, battery, wires and gator crimps. Hook the hose (12-24" long) to the front of the injector fill it with an injector cleaner, power the injector, you will hear it click open, take some compressed air (20-40psi) and push the fluid through. You can do this a couple times and clean the injector. I usually will backflow first a couple times and then flow it normally through the inlet>outlet as to inspect the spray pattern. It should easily look uniform. There's a lot more reasons why the bike might not be starting. Report back and let us know what ya find. Start with basics too, and since you've have the electronics apart a few times, stator creating power? Spark plug? TPS and MAP sensors not flipped? They can be flipped on the earlier year injected CRF250s. Blue connector is TPS. Sometimes the throttle bodies get filthy and can cause difficult starting. Clean the Map sensor orifices and tube (do NOT spray anything into the MAP sensor itself, you'll kill it) Do NOT remove the TPS sensor or you will have to set the correct voltage when re-installing. Do your best to clean the throttle body with some carb cleaner etc etc. Preferably removed from bike and do not damage the MAP sensor. Clean choke orifice, Map sensor orifice, around the butterfly etc etc. Like others have mentioned, Water temp sensor can play a role but it should at least sputter and try and fire even if the WT sensor is dead, same goes for intake temp. MAP sensor is most critical when starting, that's what the ECU uses to recognize vacuum/engine cranking in the beginning and then resorts to crank trigger after a period of time to run the fuel/ignition and trims tables. Hope this helps

-Matt