Do not lift a finger to do any work for the company during the entire 90 days. Log on to SameTime as Do Not Disturb every day. Spend ALL of your time looking for another job outside IBM. What are they going to do, fire you? Do not feel guilty. IBM betrayed you.
You're branded with a scarlet letter now and are on the Do Not Hire list, no matter how many influential colleagues you think might be able to help you stay. No one can help you.
Don't take any vacation, and insist that all accrued vacation time be awarded to you in your final paycheck. I had to fight my manager hard on this, but ended up with extra cash for unused vacation time. You might need that extra cash, I did.
Research filing for unemployment in your state and be ready to file on the day following your last day at IBM. One month severance doesn't go very far. You need to hit the ground running. I thought Right Management outplacement was a waste of time, but your experience may be different.
Good luck, keep your chin up and you WILL find a better job elsewhere, as many of us have.