Connect to Internet Via Another Computer

Alright, this maybe a little confusing, but I'll try to keep it clear.

I was posed with this question. Is it possible to connect to Internet using another computer with a different ISP.

Basically it comes down to this. There are 2 (two) ISP's within one building. Our building is primarily a learning institution, however, we lease a portion of the building to another company. The institution has its own ISP and the company that leases has its own ISP. I'm going to refer them to LI for Learning Institution and CO for company.

So I'm wanting to connect a computer from LI but using CO ISP. Basically, a proxy. With the LI, certain ports are being blocked, however, with CO it's just like a normal home ISP. So all the ports are open. So how would I go about setting up an Internet connection from LI to CO??? Would I have to set CO to a static IP and then set the computer from LI to connect to that IP?

Let me know!!!