I had a 2007-ish model Canon Powershot with 10 megapixels, 3x Optical zoom, 10x digital zoom PnS, and when I tried to take pictures of hockey games, it just became unusable. That was when I decided to get a DSLR (albeit a low-end starter). The PnS was too slow, didn't have enough flexibility, and didn't have enough optical zoom. I know you can get the last two in a DSLR-like camera, but the shutter was so slow that even at the highest ISO (having to deal with graininess and noise), it would blur the players. I bought a Canon Digital Rebel XS kit to get my feet wet, and haven't turned back for most uses. I still carry my PnS with me, but since I have taken 2000 pictures with the DSLR, I have taken only 100 with the PnS. Sure it's not as convenient, but the flexibility is amazing. I bought a low end telephoto lens to get closer to the action, and that was another good decision. I now get near-professional quality action shots. Out of about 50 pictures, I get 10 or so good hockey shots. I just took it to a family party as well, and it performed once again, wowing everyone with the image quality from our self-timed portrait.
My advice, start low, that way your investment is not as large. Don't buy a professional camera just yet. If DSLRs aren't for you, you only have lost a few hundred dollars, not a few thousand. Keep in mind that photography gets expensive FAST. Buy your DSLR body ($400-$2000), buy a lens ($100-$5000), buy another lens ($100-$5000), buy an editing program ($50-1000, or just use a free program), buy a bag ($50-$500), buy memory cards ($5-$200), buy accessories ($unlimited), buy a backup drive ($50-$800), etc. Over the course of just 5 months with my DSLR, I have invested well over $1000.