We were having the same problem with a home we recently bought - and are intending to finish the basement and have a damp corner (only had one trickle of water come in, though.) We had some estimates of putting in an inside drainage system around perimeter of room, with a sump pump - costs ranged from $5000+. First, I suggest you look at the outside of the corner that leaks water - stop the problem before it gets inside. We put in a longer drainpipe away from the house underground, also creating a gully away from that corner of the house. Also filled in an outside crack there, and used Drylok - a waterproofing paint (Thoroseal is excellent too) on that inside corner (about 10 feet on each wall leading to corner), to eliminate dampness from seeping through.
This solved our problem, a lot cheaper than the drainage system! We do live on a slight hill, which helped in our case. This may help you, but not solve your problem, is your basement completely underground?