One thing you could consider for low light action shots is using a slow sync flash. Unlike a normal flash which only exposes for the subject, a slow sync flash exposes for the background then uses the flash to freeze the subject motion. Sounds magial doesn't it. In reality there will still be some motion blur but it won't be as pronounced as if you hadn't used the flash at all. If you have a DSLR, it will be capable of using this type of flash. If you have a point and shoot, it may or may not. Also, some point and shoots disguise it as "Night Mode" so it's a good idea to read through your manual to see what it's capable of.
A couple recent
articles about
slow sync flash here at DPS.