When you installed LR4 did you allow LR 4, to create a copy of your LR 2 catalog?
No because my Lr 2 catalog is on a different computer.
OK, that's what I thought. All your work you have done with your photos (which you say is on external drive is stored in the catalog). If you have chossen to save to .xmp by choice, this is not a normal default in Lightroom, some not all your work will be in the .xmp files.
You have two choices if you have the .xmp files with the photos on your external drive.
a. Re-import the files from your external drive into LR 4 on the new computer and the info from the .xmp files will be read by Lightroom and apply to the new catlog. However lots of info that is used only in Lightroom like collections, stacks, presets, lill not be available in the new catalog. This is not the recommended approach.
b. Copy the old 2 catalog and the Preview folders from the old computer into the Lightroom sub-folder in the new computer, this is located by defsult in your main hard drive in User> Picturers> Lightroom/
With Lightroom 4.x closed double click on the old catalog file with the .lrcat (LRCAT) extention and this will open LR 4 and you should get a prompt if you wish to create a LR4 compatible copy, proceed with this and you should be good to go.
Have a read of the "Read me file" that comes with the LR 4 download package and you will be provided with full info for the process.
Thanks. I think I will try the second option.