You mean a cell phone SIM card? I've never even seen anything on the mini called a SIM card slot, just a card reader. Anyway you can unscrew and dissassemble dell laptops without voiding your warranty. Many replacement parts they ship to you for you to install yourself after all. Depending on where it fell taking out the keyboard might reveal the lost SIM card. You should be able to do a pretty limited dissassembly, following the instructions in the user manual or in this forum, to find the SIM card.