Battery died cause I left my lights on, jumped the car, sat in the car reving the engine a little bit every few minutes, then I tried to rev it up to 5500RPM but right as the needle gets to 4000, the engine sorta limps and I can hear a gentle *thump* near the back of my car, as if it were coming from the exhaust.

It's weird cause when I turned off my car and started it back up, and instantly revved it to high RPMs, it went past 4000 no problem. But when I maintain it at like 2500RPMs for a few seconds, then increase to 5000, it does the same thing again at 4000 and just kinda thumps lightly and I instantly take my foot off the gas.

Car drives just fine though, this only occurs while in neutral and i'm idling. Any ideas?

 

in neutral, the ECU prevents any revs past vtec, or about 4000 RPM, as you found out.

 

Normal function

 

revving the car is neutral is electronically limited to prevent you from losing cool points.

Also, pegging the engine at start up is not good for an engine that hasn't built oil pressure.