Never had issues before OpenVPN.
In any case, I am not sure which pieces of the puzzle were preventing us from getting this working, because it is now working completely.
So whatever was causing the problem is no longer a problem and no further help is needed.
One thing that might have been the solution: when viewing network properties, three connections were present: one called "Local Area Connection" (my normal connection that was previously in place, and with device name Intel(R) PRO/100 VE Network Connection), one called "Local Area Connection 2" (added when OpenVPN was installed, with device name "TAP-Win32 Adapter V8"), and a third irrelevant 1394 Connection.
Previously the DNS servers for the Local Area Connection were set to my ISP DNS servers, and those for Local Area Connection 2 were set to our internal VPN DNS servers (with 10.X.X.X addresses). We changed the Local Area Connection to also use the VPN DNS server IPs. This may have been a missing factor, although we previously did try that configuration.
In case this is related to the solution, this question should be PAQ'd.
Requesting refund and PAQ as we have solved our own issue.