Can’t find computer by name only by IP address

I had initially checked the host file as SilverbackNet suggested, but on a Windows 2008 R2 server this is the default file:

# localhost name resolution is handled within DNS itself.
#   127.0.0.1       localhost
#   ::1             localhost

# indicates a comment in the host file, so all the entries are commented out, and the first line is a bit confusing. I then noticed that there were two entries for localhost that were commented out, so I tried uncommenting the IPv4 one and it worked! I should have tried that first but I was thrown off track by the first line. Using the below host file pinging the computer name or localhost will always return an IPv4 address, which fixes the problem with the 3rd party software!

# localhost name resolution is handled within DNS itself.
#   ::1         localhost
127.0.0.1       localhost
127.0.0.1       VPS-Web

First of all: A domain is not listed in NETBIOS.

As Igal mentioned above, the reason that ping works against the FQDN is because of the round-robin A-records of domain controllers.

I'm guessing that your DNS suffix isnt correct on the client you're using ping from, as it fails to guess wich TLD "mydomain" is under. Please run ipconfig /all and double-check "DNS Suffix Search List".

EDIT: Actually, this only works if your AD domain is in 3 parts or more. I can get it working on one of domains who are named "lan.domain.com", but not a domain called "domain.local".