I just pulled mine out while it was on and waited 30-40 seconds and put it back in and pushed the power button to turn it back on, it booted and is working fine. Seems to work better then just a power down for some problems.
I really don't know if it makes a difference if you turn it off first or not. So far I have not turned mine off before pulling the battery.
The reason why the battery pull worked better is because you have FASTBOOT turned on. When I first got my Inspire that's the first thing I turned OFF. Turn it off and then turn the phone off, that will clear things from memory.
See how FastBoot works, is it keeps certain things in memory even when you turn the phone off, so it will boot faster when the phone is turned back on. The problem is, if you are having a problem and turn the phone off and back on, the issue you were having might still be in memory and not cleared.
I've solved some customer's problems by turning off fast boot. For example, I had a guy who's bluetooth was acting flaky and kept thinking a headset was connected even when not. He tried turning off and back on and still had issues. I turned off Fastboot and then turned it off and back on. Everything worked fine after that cause whatever was in memory causing the issue was cleared out.