Common problem with moving a system is it gets flexed, shaken etc and
sometimes components lose part of that solid electrical contact they had
when still in their original location.  This possibly could be your
problem.....if you are comfortable with doing so, I suggest you open up
the case and try to make sure that components are seated properly...pay
particular attention to any cards that are located in slots.  A lot of
problems I have seen over the years have been cured just by removing the
said cards and then re-installing them (in fact, yesterday I received a
"problem solved" from a chap who moved his system to a new location in
his apartment and lost all video....upon my suggestion, he removed the
video card and then reinstalled it. Video was up and functioning right
away).

Another possibility to consider, is that the external HD's USB
cable/connector is broken/malfunctioning....if you haven't already done
so and have a spare applicable cable kicking around the old domestic,
try swapping them. And if you have a mutlimeter continuity check the
external's cable.

How about power getting to the external.....any lights, hard drive
activity sounds etc?  If you have moved the external HD consider the
possibilities with respect to it and what I outlined above concerning
moving equipment.  If the unit seems dead check the voltage of it's
power source with a mutlimeter.  If you it plugged into an extension
cord, and/or power bar make sure the connections are tight, applicable
switches on etc.

One thing you could check also is Start - Control Panel - System -
Device Manager.  Take a look to see if there are any exclamation marks
present on the entries....if there are, it could indicate missing
drivers, disabled device(s) etc.....and may have been caused when your
system originally barfed on bootup.

You also might want to try booting into "Safe Mode" to see if the drive
is recognized there.....it may not be due to any relevant drivers not
being loaded during the boot process and is normal.  However if it is
present, it's presence may give a further clue as to what's happening
problem wise.

Would also be nice to know why the computer originally barfed but....... :-)

The last thing I'll mention concerns Vista and the installation of
Service Pack 1 (SP1).  There seems to be a spate of problems with the
service pack and USB devices but my gut reaction at this time is that
your current problems don't indicate concerns in this area are
applicable.....always good to have an open mind though.  :-)