First a little background before my actual question: I'm a student
living in an apartment with a goodsized (20' x 18') living room. I
have an old pair of Bose speakers that I inherited from a relative. I
don't have the manual for them, but on the back they say 6.2 Stereo
Everywhere, and they have a copyright from 1985.

Recently, my roommate and I invested in a new receiver for our living
room, the Sony STR-DE597, link here:
http://www.amazon.com/exec/obidos/tg/detail/-/B0001NBH2G/102-2366442-4014514?v=glance

Right now we have the two Bose speakers hooked up to it and it sounds
pretty good in stereo, but we're interested in getting surround sound.
There are two main issues with this. The first is that we don't want
to spend very much money. The second is that we want to incorporate
the Bose speakers into the setup because they're probably much better
than anything we can afford to buy new.

So, my question basically is what is the best way to incorporate our
Bose speakers into a surround sound setup for $100 or under?

When you're talking that cheap, there's little chance of a decent
system but if you don't mind comprimise then you can get the
directional sound if not the quality.

Place one of the Bose speakers as the center channel speaker because
most of your dialague and sound comes from the center.  With the extra
Bose speaker, the only way to balance that setup would be to place the
extra speaker as the rear 6th channel.

You still need:
1) Left
1) Right
2) Rear Surrounds
1) Sub-woofer

The only way you're going to find 5 speakers for <$100 is on clearance
or used.  Since you've set your budget so low, there is no real hope
of using new speakers.  That's because anything new wouldn't be likely
to handle the power you're going to want to push through your Bose
speakers without creating distortion.  Additionally, be aware that
when you mix and match center and left/right speaker brands you will
have another problem.  The specific "voice" that a brand or type of
speakers is unique to that brand or model, when you mismatch those two
sets of speakers the voice will change in pitch as the sound travels
from right to center to left and vise versa.  Also keep in mind that
speaker placement is important.  Try to bounce the sound off the wall
for larger base response an reverbant sound.

You will have to look for deals on other speakers to complete your
surround setup and just take what you can find.  The only site I can
think of with speakers that low would be ebay.

You can get cheaper surrounds brand new, but you may not be able to
turn it up as loud.
http://www.amazon.com/exec/obidos/tg/detail/-/B00005Q5WV/qid=1090355448/br=1-2/ref=br_lf_etk_ce_av__2//002-8073626-8317662?v=glance&s=electronics&n=172571

http://www.amazon.com/exec/obidos/tg/detail/-/B00006ANX3/qid=1090355508/br=1-3/ref=br_lf_etk_ce_av__3//002-8073626-8317662?v=glance&s=electronics&n=172571

http://www.amazon.com/exec/obidos/tg/detail/-/B000093CHU/qid=1090355557/br=1-15/ref=br_lf_etk_ce_av__15//002-8073626-8317662?v=glance&s=electronics&n=172571