Are you sure the SIM you are using is for the same network that the tablet is set up for? If the tablet is one network and the SIM is another, they won't work. So you need to figure out if your tablet uses a GSM or CDMA network, and then figure out which the SIM is for.
If they are both the same network type, then you may well need to either contact your carrier/service provider and have them get you a new SIM that works with your device (not all SIMs are the same) and/or contact the manufacturer of the tablet to make sure that the SIM slot isn't damaged.