Again, these are generalizations since we have no idea what you are trying to accomplish. Also, we only see the config for one side. But 'no ip routing' turns your router into a host. It's just some dumb box sitting on the wire right now. You would generally only have that in your config if you were setting up a bridge group (in which case you wouldn't even need 'ip unnumbered'). As it is, your router doesn't route and it doesn't have a default gateway. So not only are pings not going to work, but nothing is going to work.
In general, if you're splitting the same subnet with this connection, you need to bridge. If you have different subnets on each side of this connection, you need to route. You do that by enabling ip routing and
a) entering static routes pointing to the subnets on either side
b) entering default routes
c) enabling a routing protocol
I personally would go with a. If I remember correctly, you first need a static route pointing to the distant end subnet via the distant end IP (the "borrowed" ip in the unnumbered command). You then need a static route pointing to the distant end "borrowed" IP via the local serial interface. This has to do with how routers handle IP unnumbered. I don't do unnumbered, so my memeory might be failing me. But I do seem to recall that you need two static route statements to reach a distant end when using unnumbered.
If you were trying to reach 192.168.1.0 and the borrowed E0 IP was 192.168.1.1
'ip route 192.168.1.0 192.168.1.1'
'ip route 192.168.1.1 s0'
And vice versa on the distant end.
But again, these are all guesses based on far too little information. Design of even simple networks isn't simple until you know all of the facts.