psapi.dll is a tiny file which should be on your PC. If it's not found, it suggests that the fault is with Windows, rather than with the tomtom software.
Go to this page:
http://www.dll-files.com/dllindex/dll-files.sh tml?psapi
Ignore all of the advertising blurb. Just click on 'Click here to go to the download of psapi.dll'. Then click on 'Download psapi.dll'. The file will download almost instantaneously. (It's only 19.1kb). Double-click on the file to launch your unzipping software and extract the file to the System folder (which is inside the Windows folder on your hard drive). With some versions of Windows, dll files might need to be in the System32 folder (which is also inside the Windows folder). If in doubt, put it in both folders.
With a bit of luck, that should solve your problem.
Chris