Nexus won't connect to home wifi - don't want to lose my apps

I have had a nexus 7 since Christmas and it has had no problems connecting to any WiFi I have attempted. Today however I tried to connect to my home address (to which it always connects) and it is only showing a grey WiFi signal and not actually connecting to the internet. I have tried changing the ip, time and turning both it and the router on and off, forgetting the WiFi and every other 'fix' online.
I did plan on trying a factory reset but I was wondering if there is a way to back up the apps I have installed ( I don't need to keep the data or anything like that I just want the basic apps). Is there a way I could do this without having to root the tablet? I'm at my wit's end :(

If you have the settings already set to sync it would usually just re-download the apps after a factory reset. Look under back up and reset under my settings and see if it is checked in the Settings.

Is you router separate from the actual modem? Before you try the factory reset, try rebooting your modem (not the router). There should be a reset button somewhere on the modem.

Carbon will back up apps and settings for free, without need for root. get it from the play store and install on PC and N7. connect to PC with USB and you are good to go to do a backup. CHEERS!

IMHO routers can burn out after about 3 years. Try switching off router for 1 hour, then turn back on again.
If still no joy contact broadband supplier they can test you router from their end sometimes. If they supplied router may get a replacement.