How exactly did you reinstall on the new server? Did you also import System settings from the old server via an XML file? If so, you likely had a setting in there that was pointing to a D: drive path. Did the old server have a D: drive? Which API call is triggering the error?
I used the .exe installation file that you provided to reinstall it on the new server. I did import the settings for the old servers XML file but the old server did not have a D: drive nor was there anything the referenced to a D: drive in the PM Settings.
From what I can see it looks like when I first launch PM and click "Start" it does it but other then that it looks like it randoms API calls. Possibly when someone registers for a tournament, creates an account, etc.
If this helps, I did accidentally install the trial version before uninstalling it and installing the full licensed version, but I am still having the issue.
Look on the System tab and examine every setting and see if anything in the Value column starts with "D:". If nothing shows there, go to the Accounts tab and sort the list by the Avatar column. If any of those are 0, double click to see the "Avatar file" field. Make sure that doesn't point to a "D:" drive.