If your present camera has good exposure, but the subjects are blurred, you are getting close to what you need.
But you didn't tell us about your present camera.
How about a make and model.
It all depends upon how bright the lighting is in the gym.
Knowing about your old camera helps us determine that.
If you could post a sample photo, that would really help.
To post a photo, you need to park the photo somewhere on the Internet.
Then just post a link to that photo.
If you don't have a place to park a photo, open a free account on Photobucket.com and it will put 4 links under your picture. Click on the 2nd link (called "Direct Link").
That will copy the link to your computer scratch-pad memory.
When you write your message, press Ctrl-V to add the link to your message.
Here is an example:
I am looking for a camera with good image quality. I need it for sports in a gym. My camera couldn't handle the action and I got blurred subjects. The lighting seemed okay, but this too would be a consideration. My past has been with Canon and Nikon...
I will be open to any company - looking for less than $500.
If I can get results - I am good to go!!