You don't seem to understand quite how it works.
It's not as though each physical piece of us has its own gene, and that's how genes determine what we're like, physically.
There are "controller" genes.
And, one tiny mutation, genetically speaking, can have a huge effect on the resulting critter. So it could be just one tiny change that give us a much bigger brain.
I'd also like to point out that chimps are very intelligent, compared to most critters, and have relatively large brains for their body size.
As I understand it, a huge factor in how we compare to chimps is our neotony. Our maturation process is slowed way down.
This means we're born more immaturaly than chimps (women couldn't survive childbirth is babies brains were completely grown).
So, we're out in the world while our brains are still growing and maturing, and that maturation of the brain is slowed WAY down, which we're out and about, taking in all the info from our senses, and interacting with the world.
So, no, the similarity of our DNA to that of chimps does not mean we should have nearly the same intelligence.
That's just not how the DNA --> critter process works.
Here are some links for you:
http://evolution.berkeley.edu/
http://www.newscientist.com/channel/life/evolution
http://www.newscientist.com/channel/being-human/human-evolution/dn9990
http://www.newscientist.com/channel/being-human/brain