Core issue
As soon as you configure the ip routing command, the switch loses the connectivity to rest of the network.
Without the ip routing configured, the switch uses its default gateway, defined by the ip default-gateway command in order to connect from the local subnet. When you turn on IP routing, this default gateway command does not work and there needs to be IP routes for the switch in order to communicate from its own network. Due to this reason, the switch does not respond to pings.
Resolution
In order to resolve this issue, add a default route to the default gateway with the ip route 0.0.0.0 0.0.0.0 command. This command creates a static route to network 0.0.0.0 0.0.0.0 and is another way to set the gateway of last resort on a router.
Refer to ip route 0.0.0.0 0.0.0.0 section of Configuring a Gateway of Last Resort Using IP Commands for more information.
