Try cleaning the battery contacts. Perhaps they are oxidized and not getting
any current from the battery.

The XD-11 is a popular used camera.  It is probably the best Minolta
made prior to the auto-focus cameras.  Some suggest it is the best
camera they ever built.  Leica was impressed enough to use it as the
base for their R6. It was also the first camera to have both aperture
and shutter priority modes.

The camera is sturdy, and generally is reliable. The feel of the camera
is good, and the controls are generally intuitive.  Minolta Rokkor
lenses are typically above average in quality. (Minolta made their own
lenses)

Given when it was made, (first released 1977) there are typically two
protential problems with it:  The foam seals are likely shot, unless
they have already been replaced, and there can be a problem with a
capacitor that can go bad.  It is easily accessible under the bottom
plate for replacement, if that is the problem.

The seal replacement is relatively straight-forward with the proper
foam.

If the capacitor is bad, the LEDs will operate, but the shutter won't
release on the electronic settings.  It is not the only reason the
shutter might not work, but it is a common problem.

The black body will attract a slight price premium, but a working camera
in good cosmetic condition, with standard lens should get $100 to $150
on eBay, perhaps more if it is in excellent condition, and the
description is well written.

As far as your problem with not powering up, it sounds like a loose or
dirty connection, or perhaps something physically blocking the
electrical contacts at the shutter release mechanism.  The LEDs and the
shutter operate from different circuits, so if both don't work, then
there is a basic power problem to the circuits.

If you are sure the battery contacts are clean and the batteries are
installed properly, and it still doesn't work, you can remove the lower
cover to check and see that power gets to the circuit board.  

With the lower cover removed, you have to supply +3 volts to the metal
tab in the battery compartment, and negative to any bare metal part of
the camera.  

With the cover removed, the camera upside down, and the lens opening
facing away from you, the circuit board should be on the right-hand side
of the camera.  There are two different circuit board designs, but in
both cases, a red wire should come from the battery compartment to a
foil trace at the far right hand side of the circuit board.  There is a
second red wire that goes to a point near the centre of the board, that
is not the one you want.  You should measure +3 volts on the soldering
pad to which the red power wire runs. (Negative to the camera frame.) If
you don't measure +3V, you should check the battery compartment.  If you
do get 3V, then things are more complicated, and you likely need to go
to a camera repair shop.

You can also check a couple of other things from the bottom, like if the
shutter will electrically release, but the description is more
complicated than can be described here, not knowing how good you are
with electronics.

Non-working cameras for parts sell for perhaps $30 to $50.  Your friend
can decide if the repair and reconditioning is worth it for the
additional money he might get on eBay. A recently reconditioned camera
might attract a bit over $200, though it can be hit or miss on eBay.

If you really want an adventure, and feel very handy, you can buy repair
manuals for about $15 on eBay. Note that you need some specialized tools
to take apart the camera body, and some basic electronics knowledge.  
The tools can be fashioned, if necessary, but a simple screwdriver set
and pair of pliers won't do it.