theoretically, yes... may be because of a bad NIC, bad cable, or just overall "i dont feel like working with this computer" type thing (seems to happen with me all the time)
out of curiousity try switching the cables so that the crossover is on comp a and the straight is on B (if possible) then let us know if comp A goes at half speed.
if you need to buy a new straight cable, check
www.nwca.com
i have never seen prices lower (got 7 ft cables for $0.25 a piece...)