Try booting up in safe mode and clearing out the virus rather than removing ping.exe. While the ping command may be the one executing, something from the virus is causing it to run. In safe mode, minimal services are started so you should be able to clean up your system before it starts running the infected service/apps/commands.
** Edit **
If the virus is still kicking off the ping.exe, the anti-virus isn't doing the job. In addition to Norton, you might want to consider two other applications.
- MalwareBytes - Finds malware that isn't always picked up by using anti-virus applications
- Spybot Search & Destroy - Finds spyware and registry exploits
I use McAfee, MalwareBytes, and Spybot Search & Destroy on my system and when people bring me their systems to clean up, I'll install those two programs in addition to their existing anti-virus software (if they have one installed, otherwise I'll encourage them to get one).
As for the ping command, you can't be sure that it is or isn't used. I'm not a C#, VB, VC++, or COM expert so I can't say for sure that they don't rely on the ping.exe (either directly or via some library) to first make sure a web resource is available. Maybe if you put the effort into removing the ping.exe command into fixing the problem you'd get better results. If you insist on removing the ping.exe, I'd suggest renaming rather than removing. Open a DOS prompt with the RunAs and provide an administrative login/password. From there, navigate to the %WINDOWS%\System32 folder and rename ping.exe ping_hidden.exe