If the singers sound like they're using helium, that implies that you're playing the records at the wrong speed. Are you sure you're not trying to play albums at 45RPM instead of 33 1/3 RPM? If that's not the issue and assuming that you're not in the UK, it's possible that the turntable is set to 50Hz and assuming you're in the U.S., the mains is 60Hz so it will play fast. When you replaced the belt, was there more than one slot to wrap the belt around? If so, one might be for 50Hz and the other for 60Hz. If not, there might be an internal switch.
If that's not the issue, you need to get a strobe disk and light. It's a little disk that you put on top of the turntable that has dots on it. When you use it in conjunction with a strobe light, the dots will appear to be standing still when the turntable is spinning at the correct speed. Some turntables have these built into the platter, but yours apparently doesn't.
Here's a link to a free turntable disk that they claim will work with ordinary tungsten light: http://www.vinylengine.com/strobe-discs.shtml