Audio, hi-fi and car audio - Hum problem: Using an Echo Mia soundcard with a stereo system

I asked this some months ago, and appreciate the helpful responses I
received. However, I have still not solved the problem and so would
be grateful for any further suggestions.

Almost a year ago, I bought an Echo Mia soundcard and installed it in
my computer. Up to now I have not got it to work properly, suggesting
that my set-up is incorrect.

My set-up: the soundcard is installed within a new-ish Dell Dimension
PC. It is connected to my stereo via two pairs of mono leads, each
manufactured with an RCA jack on one end and a phono jack on the
other. These are plugged into a (high quality) DIN-phono adapter,
since my amplifier has five-pin DIN inputs and outputs. The amp
operates at DIN level (a lower signal level than the line level used
by modern equipment) and is a Sugdens A48 made in 1976. The soundcard
is
connected to the amplifier via the Tape input/output.

When connected in this way, there is a near-constant hum in my system,
at a level high enough to be distinctly irritating. When the
soundcard outputs are connected to the amp, the hum can be heard
through my loudspeakers, whether or not the computer is turned on (so
long as it has some kind of connection to the mains power supply:
there is even a hum when the computer itself is unplugged but
connected to a monitor that in turn is plugged in). The computer is
normally connected to the same power supply as the amplifier, and so
they should
be grounded at the same level. In fact, all components are plugged in
to the same "surge protector" that supplies 'clean' electricity.

Similarly, whenever the amplifier is connected to the soundcard's
inputs the signal that it receives includes a constant hum, so that
any recordings I make with it from my sound system are marred by the
hum that is recorded along with the music.

As some of you have suggested, this seems to be a ground loop problem,
although it is not obvious why it occurs when all components are
plugged in to the same power supply. (It occus when the set-up
consists ONLY of amp and speakers with computer, with everything else
disconnected.) Using my very ordinary digital multi-meter, I was able
to measure a small but constant potential difference (voltage) between
the connection jacks on the amp and on the soundcard. I could not,
however, detect any current flowing.

I tried using an ordinary wire to connect the back of the amp with the
soundcard in the hope of dealing with the ground loop, but this made
no difference at all. I have not yet acquired a ground loop isolation
transformer (as suggested earlier): would this not introduce
distortion into the system? The whole point of getting an up-market
sound card was to enable me to make digital copies of music from an
analogue source without otherwise messing about with it.

Is it likely that my amp is somehow incompatible with the soundcard?
So perhaps my best option is just to get a modern amplifier?

With thanks for your thoughts.

I have not yet

Please let me know if you have any suggestions for reducing or
eliminating the hum.