if you were using a legit non pirated Total Recorder
then there shouldn't be any problem migrating the installation to a new computer.
It was the first audio software I ever purchased nearly 10 years ago
on the understanding that it gave entitlement to free updates
for the lifetime of the product.

The only difficulty I ever encountered was on a couple of occasions when
the latest update required a new password,
and I'd forgotten the original email address I'd used to register.
but I eventually found the required info and emailed High Criteria
for my new password for the latest version.