For starters I'm trying to do this from a Windows 7 box to a Windows 7 box.
I know the simple answer should be to enter \\computername where it says "Select Counters From Computer". Trouble is, every time I do that I get an error message that says "Unable to connect to machine"
I know the machine is out there and accessible, because I can bring up windows explorer and enter \\computername\c$ in the explorer bar and then can browse their c drive. So the machine is out there.
Are there special permissions for perfmon? Is here a service which needs to be running on the remote machine?
You need RPC between the machines. The endpoint mapper is TCP 135, which then negotiates high-numbered ephemeral ports on which to send subsequent traffic.
Check your firewalls, both hardware and Windows Firewall.
\\computername\c$ works because it does not require RPC, only TCP 445. (AKA Direct-hosted SMB.) And since you can access an admin share, it's safe to assume that you already have administrative permissions on the target machine.
Also I suppose you need to check the RPC and RPC Endpoint Mapper services on the machines, but I assumed those services are running since you'd be having bigger problems if they weren't.
Not if you can get to C$ - this is a admin only share. I notice you only put one slash at the beginning of your NetBIOS name. Have you tried \\computername\c$, or even just computername.domain.com (or whatever your domain is)? The later will remove any name/address issues.