I need to know how to go about checking to see if my mother had 401k

If you are the executor of her estate you should have access to her financial records, so look through her files for copies of old statements. Also, over the next few months keep monitoring her mail - if she has a 401(k) the plan administartor should send out a statement at the end of each quarter, so one should have arrived a week or so ago to cover the 3rd quarter, and you can expect the next in mid-January.