How about a battery pack for power, but then you would have to figure
out how to create a 24:00:00 timer. Maybe some sort of simple timer
that could somehow trigger the shutter - via an electronic cable
relears or infrared remote. Not sure.

What's your budget for the project?  You'll need a control system for
the camera, such as an intervalometer like a Pocket Wizard to trigger
the camera, but the real problem will be power supplies, leaving the
camera on for the duration or a way to wake it up (are there models
that have silent modes?) before it meters the scene and releases the
shutter.  You may have to add a large battery with additional voltage
drops controllers. You should look up some photographers who do similar
work, often remote video system, such as wildlife biologist. The last
thing you'll need is a hidden, secure, weather-proof box (see NEMA
enclosures).  Good luck and keep us posted.

Any motorized film point and shoot can do this if you have an external
timer to fire the camera.  Unlike a digicam, film cameras draw no power
when sitting idle.

You should be able to find an engineering student who can wire the
timer to the camera or to the camera's IR remote release.  Ask the
student when was the first time he/she rebuilt a car engine or if he
is/was a ham ... if the answer is zip then find another student ... many
engineering students can't tell one end of a soldering iron
from the other even after repeated tries.

The same student should be able to whip up a 24 hour interval timer
from some micro-power single-chip processor and a couple D-cells.

There are web sites with instruction for modifying P&S cameras
for game tracking.

Buy the camera on eBay ... with digital the rage folks are selling
their old film cameras for pennies on the dollar.

 Canon dSLRs, even when turned on, will go into a sleep mode that is VERY
light on the battery, and with a half-press of the shutter button, they're
ready to go.  (other makes/models may do the same.)  One of my friends
doesn't even bother to turn his camera off, and even with much more shooting
than you're planning on, only recharges every few weeks.  Assuming that the
same can be accomplished via the wired-remote port, all you need is a timer
to trigger it.  At the cheap end, a 555 timer circuit could be put together
for $20 that would run virtually forever on a 9-volt battery.

 If you're really worried about power, with a small sealed-lead-acid
battery, a voltage regulator, and a small solar panel or two, you could
leave the thing running for half of a decade, at least from an electrical
standpoint.  Storage, mechanical failure, and weather, however, would have a
say.  Of course, with the power-sipping nature in the sleep mode and only
one exposure per day, a $15 7-AH battery would probably have enough juice to
run the camera for a year or more, the solar panels would mostly be there to
counteract the self-discharging nature of the lead-acid battery.

 Hmm... that actually sounds like a fun project.  Maybe I'll keep my eyes
open for a cheap camera to do something like that with... it surprises me
how much even old D30s (not 30Ds) go for.

steve