Will a new router solve my connection problems?

The Set-Up: I live in a condo and use a Wireless G router for networking. I am in the room farthest away from the router and there are two walls between us. The connection drops frequently and the speed leaves a lot to be desired at the best of times. The router is a fairly old and cheap Trendnet model which gives me a lot of trouble anyway.

The Question: Will getting a new, Wireless N router help at all? Are the metal studs in the walls the cause of the problems, or is it the weak router? My laptop doesn’t have a Wireless N card, can I reap any of the N benefits?