Well, from the sounds of it, it is entirely possible that the two
pickups are wired out of phase, resulting in cancellation and signal
loss.

If the centre position sounds nasal rather than sparkley, then that's
the culprit. As an aside, I will point out that when pickups are wired
out of phase, you can reduce cancellation (and bring back the
volume, ironically) by nudging the volume control for one of the
pickups a bit. This occurs because the two pickups need to be
relatively matched in signal level and spectrum to cancel optimally.
If the signal level of one is reduced, then they are less matched and
so cancel less.

In other words, if it has twin volume controls, you should be able to
get back some of the body by turning one pickup's volume control
down a hair (e.g., from 10 to 8). You'll be able to resume
cancellation any time you match pickup levels (i.e., it doesn't need
to be at full volume to cancel, you could have 7 + 7). 

   Two pickups in parallel, correctly phased will not sound as loud
or as full as just a single pickup. If the middle position is
humcancelling (plug your guitar in near your computer monitor and
switch between the 3 positions to see if the noise increases or
decreases in the middle position) then the pickups are probably
phased correctly. Now if the noise *increases* in the middle
position it doesn't mean that the pickups are out of phase; unless
one of the pups is RWRP with respect to the other, the noise will
increase with both pickups selected... (An out of phase sound is
very thin and "whiny"; once you hear it you will never forget it!)

    Fender is selling a 4 position Custom Shop Tele selector switch
which requires that a separate ground wire be connected to the
neck pickup. The 4th added position is the two pickups in series; if
one of the pickups is RWRP then this combination is humcancelling
and a very welcome addition to the Tele pallette.

--Good luck!

Steve Ahola