Use snmp to monitor the process remotely.

On RH Linux the command would be

Snmpwalk –c public hostname hrSWRunName
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This will return all the process names and PID running on the windows machine in the following format.

HOST-RESOURCES-MIB::hrSWRunName.1234 = STRING: “foo.exe”
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From this list it should be easy to parse out the name you want. This will of course require that you run "snmp service" on the Windows machine if they are not running already. You will not need to run the "snmp trap service" however.

-- UPDATE --

Net::SNMP will be the package you want, and Example 1 in the docs will work on a windows machine.