I had an issue after backing up and restoring the DB's from server to server, We have since had some issues with missing information. Is there a way at this point in time to know if the databases were restored fully? Are there log files anywhere?
If the restore completed, then the database was restored fully. What kind of backup did you take (show the code, or explain the steps if using a 3rd party tool or SSMS GUI)? How did you restore that database (show the code, or explain the steps)? What information was missing?
This answer and the link to Paul Randal's article will help explain how a full backup happens and should answer your Are the log files anywhere question, assuming you did a Full backup. You can, of course, do transaction log backups too. - scsimon
I've seen cases where backup was done appending to the file and then restore was done from the first file (which is default) from that file. I.e., restoring not-the-latest-backup. Check using
RESTORE HEADERONLY. - tibor-karaszi