Activation Code

OK im new here i know a bit about computers . now my problem is that i have a dell laptop and its my mothers own and when i used it i would see this key at the bottom of the toolbar but i never knew what it was it would just count down the days i had left i tried looking it up tried double clicking it right clicking it everything and now the days are up and i finally found out what it meant but i found out to late it was tellin me the days i had left until i needed to re-enter an activation code now i looked all over the laptop and there was no product key so is there anyway i can activate it or find out the activation code product key without having to buy a new key ? i dont have the cd's to re install windows can anyone help me?