I'd give this thread a read
http://forums.sv650.org/showthread.php?t=120718 might give you some help.
It should be easy to get it into neutral when engine is running. Just a gentle tap up on the gear changer from first.
If you think its something wrong with the bike, i'd recommend doing an oil and filter change first. That'll most likely cure the problem. Its a pretty simple job to do. I'm a novice and managed to do it. Although i did flood my garage floor with oil
