It depends on the tablets settings. If it allows you to fix an IP address for it, do so - starting with the same three numeric blocks as the router's gateway so if that is 192.168.0.1, allocate the tablet the IP of 192.168.0.3. We need more details of your tablet to be able to find the problem. I can only find reviews whch aren't too specific but my Gingerbread Android phone doesn't all me to fix an IP.
I hope you re-enabled wireless security, having proved it isn't the problem.