Hello Primoz,
You have got ip route disabled:
no ip routing
It has to be enabled:
ip routing
Aside from this I would enable CEF as we can see high cpu without it (it will impact the performance of the router at least):
ip cef
and on the interfaces (gig0/0 and gig0/1):
ip route-cache
One more note about the config. You have got the default route pointing to the router's own interface. This will create a connected route and we will ARP for every destination IP which does not have an ARP entry which is not very efficient.
I would recommend to reconfigure the route command so that you either use the next hop router's IP address (if you know what IP the ISP is using) or you use the dhcp keyword at the end of the route.
I hope it helps.
Warm Regards,
Rose