First of all the TeX filter (and the debugger as well) do
not depend on Perl in any way, only on the mimetex.exe executable. The algebra filter depends on Perl as well as mimetex.exe. So first you need to get the TeX filter working.
First of all are you sure that you are running texdebug.php not algebradebug.php?
And you are getting the error message "This program cannot be run in DOS mode", when you click on the Show Image button?
What happens if you open up a command window on your
server, navigate to the folder containing mimetex.exe, and then manually run mimetex.exe in the command window? You shoud get an ascii test pattern in response. If you get the above error message instead, then the likely cause is that you have a corrupt mimetex.exe, e.g. from transferring the file by
ftp in text mode instead of binary mode.
The TeX debugger will also display the size of the mimetex.exe and an md5 checksum of the file. What values are displayed?