with Daisy on removing all the dead twigs. Wire cutters work fine if you don't have some pruning shears. Personally, I wouldn't cut off any green stems, let them grow for a while. The foliage you have looks pretty healthy, actually, and will help the plant to recover. Once it's growing and looks better, you can trim and shape it to whatever you want.
Looks to me as if your room mate let this plant dry out and thought it was dead. Amazing how resilient plants can be, huh? I think you've already saved it. Anyway, put it near a window, water it for a few weeks and see how it comes along. If it keeps growing, post another picture and maybe we'll be able to ID it for sure.
You'll need a little bit of fertilizer to give it, since we're heading into summer. Get a little box of soluble fert, (you dissolve it in water) and give it half strength (i.e. use half of what they say on the box) about every 2 weeks until you're sure it's going strong. Then go with full strength.