At first I thought it was a net problem, but I can get into gmail on my wife's computer in the next room and we both use the same internet line.
Any ideas what the problem might be?
Two different computers from the same IP address trying to log in to two different Gmail accounts...especially if one of them is already logged in to one account. Thus the infinite "clicking away" on the other machine trying to login on the same line to a different account.
If you can log in to your account on her machine, you must necessarily log out of her account first.
P.S. Once you are "signed-in" to Gmail or Google or any of their services, your machine is signed in. Look in the upper right-hand corner of the screen. You'll need to sign-out to sign out of all Google services. (What I mean is, if your wife signs into her gmail and then starts surfing other sites, say here for instance, she's not logged out from Google or Gmail and this non-logout may be what's futzing up YOUR login from another machine on the same line.
Try having your wife log off her gmail account on her machine and then you log in to your account on your machine.
Does that work?