If you can put a small VBS file in the startup folder then this will be a breeze. Once the computer's annual check is complete, place a file called "timestamp" in C:\annualcheckup\ on each computer. It doesn't have to contain anything, except maybe a message saying something along the lines of "DO NOT MODIFY", etc. Then, place the following code inside a .vbs file (name it anything you want) and place it in the users' startup folder.
Set objFS = CreateObject("Scripting.FileSystemObject")
strFolder = "C:\annualcheckup"
Set objFolder = objFS.GetFolder(strFolder)
Set strfile = objFolder.Files("timestamp")
if datediff("d",strFile.DateLastModified,Now) >= 365 Then
'notice on year
msgbox "Your computer is due for its yearly check."
If DateDiff("d",strFile.DateLastModified,Now) >= 355 Then
'10-day notice before year
msgbox "Please remember to return your computer for a yearly check soon."
end if
The code will check to see if the file is 365 days old, then tell them they're due for a checkup, and if it's later than 355, then tell them to remember that their yearly check is soon.