Final Word: It would help to know what your talking about, an i3-2100 is not some busted dual core from 2005. It is true it doesnt hold the weight of the i5-i7 series it is still very strong in gaming and general use, especially on a budget. It also acts as a quad core while encoding so your just completely wrong on his pc not being good enough.
@op 720p really should be fine for you but as said check a different server, anything hindering data flow basically is like a car backfiring. Also just because you have 10up and down doesnt mean your sending somewhere that can accept anywhere near that fast