Sorry, HM1 doesn't create such a log file.
Which Operating System, Firewall, and Anti-Virus are you using?
For W7 and Vista you must set \holdem manager\dbcontrolpanel.exe, holdemmanager.exe and hmhud.exe are started as administrator. Run the windows explorer and navigate to your Holdemmanager installation directory. Right click the executables and select properties... then select "Run as admin" from the compatibility tab.
Add exceptions to the windows firewall for holdemmanager.exe and hmhud.exe, even if the firewall is turned off. If you have a 3rd party firewall, do the equivalent or uninstall it temporarily.
Make sure your video card drivers and windows auto updates are fully updated. Run a manual Windows Update and install all updates, including all .net framework updates.