I think it is possible, although it will take some work to capture the info from both installations.
What you'd need to do is use the Additional Tagging & Reporting Tools to save all the data from the old computer as a report. Do the same with the new computer. Combine your data sets using something like Excel or Google sheets to get total play counts.
Then you can use additional tagging & reporting tools again to transfer the numbers back into the files. I strongly suggest using a custom tag for this, so that you can verify the numbers match up with the right tracks. Once you're sure that's correct, use additional tagging & reporting tools a final time, to copy the new play counts into the official play count field.
(And the next time this comes up, you can save your play counts to the custom tag before moving your music files, then load them in at the other end so you pick up where you left off.)