ICMP traffic (pinging) is on a completely different OSI layer than DNS (name resolution) as long as you try to connect to your host via IP DNS related problems won't manifest.
If you can connect via IP but not via host name then you can start thinking about a DNS problem, but it is best practice to have correct forward and reverse lookup configuration in your DNS server for the host. So myVMHost.myCompany.com should resolve to the correct IP in an ideal world.
For your case start with the standard troubleshooting.
Step 1 - Already done, you cannot reach the outside or your standard gateway via ping.
Step 2 - Double check the NICs and cables (do you see lights on the NIC ports and switch ports)
Step 3 - Double check network settings configuration like subnet mask and VLANs
Step 4 - Look for incoming packets on the switch (if it is a managed switch), are those dropped, are any packets received at all
Step 5 - Try plugging a laptop into the switch and configure the ports accordingly, can you ping the host now, can you ping the laptop from the host