If shooting indoors without a flash is the important thing, I'd lean more towards one of the Fuji cameras like the S6000. They have much better high ISO performance and are thusly more suited for low light shots. I don't believe they come with a stabilizer though, so you might find that you have a harder time taking shots at extreme telephoto without turning up the ISO a bit.
If the Fujis don't appeal to you, then it may be time to start shopping for a DSLR. Pretty much any of them will perform significantly better than the Canon, but in particularly the entry level Canons, Nikons and Pentax cameras are excellent. You can get the Pentax K110D with a kit lens for around $400, though you'd have to spend another $150-200 to get the long range zoom as well (there may be rebates available though).