You should be able to copy across the GP application folder. But, I'm not sure that this is your issue.
It seems that the table definition for the UPR table seems to be different on the old and new servers.
Eithre the tables are actually different - or you have a different version of GP installed on the new (when you run a process, its trying to update / read from a column in a table, and it cannot find that column.
Certainly a second attempt at the transfer is on the cards.
In terms of the GP application folder - you should be able to install GP on the new server, and then copy across the contents of the Old GP application folder and overwrite what you just installed. (After you do this - search for any .cnk files in the application folder and delete them - otherwise, the first time you launch, these .cnk files will try and create new dictionaries)
This will ensure both GP installs are at excatly the same version. If you install in exactly the same folder on the new server, then you shouldn't need to change much once you copy over the old files - just maybe the Dynamics.set file.
Then if you set up SQL exactly the same as the old, same collation etc, and attach the databases, when you launch GP and connect to the new server, you should be OK.
Verify that your ODBC settings are correct - SQL Native Client, no tick boxes ticked etc.
One thing you could do after you copy the SQL data across is to do a 'select * from that UPR table' in both SQL's - and compare the column names.
Also, can you set up a new ODBC on the old server that connects to the new server? If you can, then you can rule out the GP application from the issue - if you can connect to the new server from the old GP application and still get the same errors - then its probably not GP? - its got something to do with how you are transferring the SQL databases across.