It really depends on what IC's you need. For one, you could try eBay. Just look for sellers near your area and check to see that they dont charge a ton for shipping. If you are looking for specialized IC's, Maxim (www.maximic.com) is very generous about samples and doesn't charge for quantities of up to 4 IC's.
if it is for school, get your prof or lab manager to request samples of the parts. or just ask the lab manager, they might have them in stock already. my old college had a real big lab support dept, all sorts of ics, passives and whatnot in stock to support the ongoing classes.
You could find a local robotics/electronics/ham club, and look into joining. Often these groups will do mass orders from, say, DigiKey, thereby getting order prices up above the break point for the shipping charges and spreading the remaining overhead cost among several members.
You have to find a way for the sponsor to benefit from what you do, convince them that you do have reslults (something that really helps is having a previous thing to show to them), and be very business like about it, because that's what your sponsor is...a business.
It is VERY hard to find a sponsor, since they don't like to sponsor individuals. What I would do, is to Dumpster diving, or go looking for broken stuff. Then pull the parts off the board as you need them. I used to do that, and it can help you.