Need advise on whether to upgrade lens or body

I've currently acquired an Olympus e620 from a family member. I have both the 14-42mm f/3.5-5.6 and 40-150mm f/4.0-5.6 stock lenses. I was a point-and-shoot photographer but have loved the upgrade to this body. I've now taken a couple of DSLR classes and have gone to shooting in manual. Before this camera, when I felt ready for an upgrade, I purchased an Olympus XZ-1 for its size and performance. But now I'm happy to have an interchangeable lens body.

Now to address the problem I've having. The e620 has very limited low light performance. I know the big problem is the use of stock lenses and I need a faster lens. For example my XZ-1 has a fast lens and I end up taking all my indoor pictures with it. But I want to use a DSLR to get a little more out of my photographs. I rarely use a tripod because I'm usually on the move and taking pictures of my 8 month old. So lowering the shutter speed just causes me to have blurred photos and I hate even the slightest amount of movement blur in my images.

So this is my question to the forum members: Is it worth spending the money for faster lenses for the current M4/3 e620 body I have, or should I sell the system I have and look to upgrade to a new system and body? I've always been a fan of Canon in the past and would probably look for a new system in their line. I just don't want to dump a bunch of money into lenses for a micro 4/3 system if I will need to eventually upgrade down the road.

Any suggestions are welcome, and if you think I need a lens for the body I have, what would you recommend? And if you think I need to upgrade to a new body and lenses, what would you recommend? I don't have $4,000 to dump into an entire new setup, but maybe a new Canon t4i system is a good start? Let me know what you think.