Camera Shopping

I'm wanting to invest in a new camera ... but really have no idea where to start!

A few things about my "photography style":
- I'm by no means a professional photographer nor do I inspire to be one, so am pretty clueless when it comes to all the specifics and terms used in the biz
- I'm very much a "point and shoot" kinda gal, I can handle different settings, but prefer if I don't need to tinker and tweak to account for changes in lighting, etc.

I'd like something digital, and a video option would be nice though not required. I mainly take pictures of the dogs, so the ability to take nice action shots is what I'm really after!

I'm currently using a Sony Cyber-Shot DSC-T33. It's decent little camera, but really isn't all that great as far as low lighting situations or action shots. If I want to get a nice picture, it basically has to be a still shot, outdoors, and between the hours of 10am and 4pm. Late afternoon/evening lighting isn't enough to allow me to take a good picture. And anything other than absolutely ideal lighting means that I can't take action shots. Things are just too dark. And taking pictures with standard indoor lighting is completely out of the question!

So what would you suggest for a digital camera that:
- won't break the bank
- is easy to use
- takes nice pictures in low lighting/indoor lighting
- takes good action shots in all lighting

Either brand/makes would be good, or specific requirements that I can look for in different makes. You know, those fancy terms and numbers that I don't totally understand.

I've had a few people suggest brands/makes that they like, so any comments on these options are also appreciated!
Canon Digital Rebel XT - Looks wonderful, but might be a bit too much camera for me.
Canon PowerShot S5IS
Olympus Stylus 1010
Canon EOS 450D
A variety of Nikon CoolPix
Nikon D40
Canon SX100 IS