The 13 digit key is your your local wep/wpa key for you to connect to your wireless signal. If you have wep/wpa security on your wireless signal you should have to only configure your laptop/PC to see this once and it is then remembered in the config for your wireless setting.
The 4 digit key was/is either
A) the password for your router to connect to your ISP (which I know BT require as they use PPPOE) or
B) the password to get on to the administration of your router which was 0000 on some routers so Im guessing this is it.
If someone got on to your network and typed 192.168.1.1 into their browser they could get on to your router admin pages and do funny stuff if they wanted by typing in the default username (admin?)and password(0000) for the router.
so as this is probably the case, get on to your routers admin pages and change the password. google for instruction on how to do same for your model router.
you may need to configure a new wep/wpa key as well if it has reset to off, again, google for your models config settings.