Assuming your data is company CE consisting of *.BCE data files located in a DBAMFG\CE folder on the old server, do the following:
 
1.  Make sure that both the new and old server are running the same version of DBA.  If you have IS Tech updates installed on the old server (not sure if you are a subscriber or not) you will also need to install the IS Tech update to the new server.
2.  On the new server, use UT-I to create company CE which will create the DBAMFG\CE folder with empty data files.
3.  Copy the \DBAMFG\CE folder from the old server to the new to bring over your data.
4.  Password security is stored in the Default company which is the *.B files located in DBAMFG\DEFAULT on the new server but either in DBAMFG\DEFAULT or in the root DBAMFG folder on the old server depending on how long ago you originally installed DBA.  In any event, those files need to be copied to DBAMFG\DEFAULT on the new server regardless where they were on the old server.
5.  If you have modified any forms you need to bring the *.RTM files from the DBAMFG folder on the old server.
 
 
Alternative approach - Since you already have Pervasive installed on the new server, copy the entire DBAMFG folder and all subfolders from the old server to the new server and it will bring everything across.

You are quite right, I left out a step - if you are running PSQL Workgroup as opposed to client/server then you need to reset the gateway to get past the error 116 - at the server, C:\DBAMFG\GATEWAY.EXE
 
Glad you are up and running.  Now that you have the new server installed, consider the program updates available from IS Tech Support!!!