Are the VMware tools installed on the VM level, or is it at the player level - that is, it is common to all VM on a given host?
When VMware Player is initially installed it's done so without VMware Tools installed. Typically when you install a Guest OS in a Virtual Machine and you choose to install VMware Tools, or during an Easy Install, if the appropriate VMware Tools ISO Image hasn't been downloaded from VMware then it's downloaded and installed on the Host. As an example you install VMware tools in a Windows Guest then VMware Played downloads an executable from VMware's Server and when this file is executed in the background the windows.iso file and the windows.iso.sif file are extracted to the working directory of VMware Player. The windows.iso file gets attached to the VM's CD/DVD and then VMware Tools gets installed in the Windows Guest. The installation on the Host and the installation on the Guest are two separate processes. The install of VMware Tools in any given VM is not hooked to any other VM as each VM (other then linked clones) are totally separate and apart from each other and by default have no bearing on any other VM as far as it's install goes. Obviousy if you have limited RAM and are running multiple VM's the it can have a performance impact on each other however creating a new VM and installing an OS in that VM has no bearing on existing VM's provided you didn't add an existing virtual hard disk from an existing VM! 
As for the second part of your answer you probably right... the message is:
Bad Image (error code c000007b)
The Application or DLL \??\c:\windows\system32\DGI32.dll is not a valid windows iamge. Please check this against your installtion diskette.
Well, have you done as the error message suggests?