Desktop and Stereo Overloading a Line?

I hooked up a line out on my new desktop PC to the auxiliary in on my
650 watt stereo.  Everything was great for a day or so, then my
computer froze.  Because I didn't know these new computers turn off
when frozen by holding the power button in for a few seconds, I
eventually unplugged the computer.  Then I plugged it back in.
Sometime between unplugging it and plugging it back in, half of my
studio shorted out.  The other half remained on.  Afterwards, the CPU
was messed up, and needed replacing.

The apartment handyman said that one of the two "lines" in my studio
was overloaded, and that I could rectify the problem by balancing the
usage of the two lines, and possibly by switching the main from 15
amps to 20 amps.  A clerk at a tool shop where I bought a receptacle
tester agreed that it was line overload.  But, I did shift things
around, and still, I had one episode of one half of my studio browning
out for a sec, and the other blacking out for a second, after which I
gave up, and am now only using my stereo when my computer is not on,
and vice versa.

Since adapting this policy about a month ago, no power problems have
ocurred.  In the two or three years before I got the desktop, I had
the stereo hooked up to my laptop, and never had such power problems.
About 7 years ago I had a similar stereo hooked up to a desktop, in a
share-rental house so dated it only had one non-grounded outlet in my
room (I used a grounding attachment), and I did have similar power
problems that were resolved, IIRC, by not using the stereo with the
computer.  My current studio has 11 grounded outlets.

I figure there's got to be something I'm missing, a way to use both at
the same time without risking harm.  I counted the amps up (including
refrigerator, et c.) as best I could, and it doesn't seem like I was
ever using 15 or more amps.  I was only running two laptops, a
printer, the stereo, the desktop system, a few generic, power-sipping
gadgets, and a few studio standard lights (no dishwasher, oven, or
A/C).  Plus, I see people all over the place with home entertainment
systems much bigger than my stuff, probably running with A/C and
what-not, and I never hear of the problem I'm having.

What can I do?

Thanks,
Keith