If you had a CD player in the system, then it may be easier to find the problem. A CD player has fairly consistent sound quality, in comparison to a computer, or TV for the source. I'm not too knowledgeable about computers, but the ones I've used listening to something off of the net, can vary a lot in my experience.
A TV can be inconsistent with sound and picture also. When I hear a commercial on one channel, it may sound good. Hearing it on another channel can give good, or bad results. So a TV doesn't always help in finding a problem.
Then the computers themselves get moody, and change at times. So I'm thinking something more consistent like a CD player, or DVD player may help in this case.
You mentioned streaming YouTube. If you download something that sounds good to you using RealPlayer may help a little. When you get this sound problem, play that video that you downloaded to RealPlayer, and see if it sounds OK. This isn't as good as a standalone CD player for consistency, though. But still, may give you more of an idea.
Using the output from a computer using these (streaming) sources you mentioned don't have the sound quality, like a CD does. All of my computers own sound outputs, vary a lot too. Even if I play a CD in them.
Your speaker and amp combination, is probably really accentuating any small problem.
A poor connection is a possibility, but you are using two different sources (TV and computer), with separate cables for each. So, I'm thinking the odds are slim that both are making a poor connection, since this problem existed, since you bought the system.
I guess what I'm still saying is a CD player, DVD player, may help a lot in finding if it's your system, or the inconsistent (computer/TV) sources you're using, causing your problems. If you don't have a CD player, see if you could get one for testing. This is the only other thing I can think of, since its sound quality way more reliable, especially using the same good sounding discs. Other than this, I'm kinda out of ideas. I hope you find an answer to this.