Have setup a vmknic for management on a internal only vswitch (ie no uplinks)...and have a software router VM straddling the internal vSwitch and another vSwitch that has access to uplink...routing enabled
I assume the subnet on the internal switch is different than the subnet of the uplink - is this correct?
Now if we need to use the internal vmknic as host ip address for vCenter management ...assuming the default gateway of esxi was previously pointed at the gateway of uplinked network and esxi can have only one default gateway which of below 2 approaches is advisable
The ESXi gateway should be pointing to the software routers IP address on the internal vSwitch and as the routes are deifined in the software router than you should be able to connect the ESXi to the vCenter server.
In regards to responding the VMKPING issue - it might be that the software router is set not to repond to an ICMP request as a security measure - are you able to ping from the external network to the internal IP address? Try running a tracert to the VMKERNEL IP address and see where the packet is dropped.