This is what I would do:
Ask for the complaint against you to be made valid, which means the following. Say in your written documentation that you want the following written in a formal letter to you. 1) Date of incident 2) Time of the incident 3) Name of person who has made the original complaint 4) When was the original complaint filed? (and you should request to see the original documentation or to be given a copy of the complaint.) 4) The nature of the complaint--Were you supposively rude or incompetent or dangerous or what?
If this information is refused to you, then I would...
Write up the conversation as you remember it.
Mention that the complaint against you is heresay. The word heresay is important as heresay implies that the complaint does not hold water. The complaint does not mention you by name,only by description. Does the complaint mention a time that you were supposively playing on the computer? Can anyone else that was there vouch for you and what you were doing at that time? Housekeeping, dietary, co-workers? What about your charting? We do computer charting and that always shows what time it was when you were charting. (For that matter, does your place of employment have computer techs? If so, they can go and find out exactly what the activity was on that computer at any given time.) Point all of this out in your written documentation. Defend yourself at each step. ie "I never use the computer at work for recreation purposes as a matter of ethical principle and in agreement with my employment contract."
Either the complaint will be dropped or formalized against you. If you do not hear anything further, then I would, after a month, write another letter which states that since you have not heard anything further on the matter that you as of this date, consider the incident closed and expect that it will not be commented on further. If the complaint is formalized against you, answer each charge as best you can and include documentation, times, and witnesses' names as best you can.
If you use either of these methods, you need to mention in your letter that you are requesting that a copy of your letter be put in your personnel file and that you will be keeping a copy for yourself. Then make copies of the letter and SEND, by certified mail, if necessary to all interested parties--You supervisor, your boss, and Human Resources and whomever else might need to know. (ie the people "downstairs").
I know this probably sounds over the top, but it is the way to go to protect yourself. Do not let this come back in a year and bite you! Either they need to formalize the complaint against you or drop it. Your professional reputation is at stake as well as future job prospects. GOOD LUCK and hang in there!!