Real receivers start at about $100 (for 2 stereo), HT receivers at about $150 (for a "no name" or "house brand" like Insignia) and $200 for a brand-name, entry-level 5.1 HT receiver. So that's at about twice your budget with the speakers you have in mind.
The good thing about your plan is that it gets you an audio upgrade now within the constraints of your budget. The downside is that if you want to go to a full HT system later, you'll pretty much have to replace everything you buy now and start from scratch. Does the T-amp even have a subwoofer output?
I can't tell you what might be wrong with your current setup. The only real test is going to be hooking up the T-amp and either the computer speakers or your final speakers (or a couple you borrow from a friend) and seeing what happens. If the same problem is there, check your TV settings. (Some devices do strange things like not down-converting digital audio via the analog outputs if you have digital audio enabled - which might be one explanation for what you're seeing.) Then call the store or the manufacturer about a warranty repair. If the sound works then there was some quirk with your current setup and it probably isn't worth your time trying to figure it out.
Regards,
Joe
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