My guess:

a) Max232 has some unused pin, so it is floating causing lots of noise
at the Max unused output, so to the supply.

b) There is a wrong connection at the Max, even that it is working, as
for example, a wrongly grounded pin.  Read here also wrong
capacitors...and connections

c) Missing 200µF + 0.1µF capacitors at the +Vcc

d) Missing a 10 Ohms resistor in series to the INA122 Vcc with an extra
decoupling 10µF capacitor at the INA122 side... filtering noises...

e) What is the voltage *before* the 7805? Isn't that too marginal close
to the 5V? (when you remove the max, reduce consume, 7805 input voltage
goes a little bit up and it regulates ok.

f) Try to feed power to the Max from any other +5V except from this
7805. 

g) Max generates some oscillation noise from its charge pump, but not
enough to create problems to the INA122, except if you have a terrible
grounding problems.  Try to route another ground wire from Max to PS
(PowerSupply), another from the PIC to PS and another from the INA122 to
the PS. Avoid to use "Bus Ground Sytem", go to a "Star Ground System"
(single ground point for analog and another single ground point for
digital, then a single wire connecting both grounds).

we are starting to get curious now.. <g>

Wagner.

Greg Hartung wrote:
> 
>    Well, I connected the pressure circuit back to the PIC board, and it immediately
> stopped working correctly so I started pulling things until it did work.  This board
> has an LED, a piezo, a 7805, a 16F877, a 20Mhz ceramic resonator, a relay and MAX232.
> Removing the MAX232 did the trick, but the MAX isn't connected at the other end during
> this problem, only to the PIC and the MAX works just fine when it's in the board.  I
> reread the MAX datasheet, and I don't see any glaring mistakes.
>    I have absolutely no idea where to go next.