Qualifications for this response ... not a certified DB person, but have run many moodles over the years and for a variety of entities.
My 2 cents ...
In the new site, delete rows 3 -> in mdl_user table. That will leave you with ID 1 ... which is guest ... set to manual ... do not remove. And ID 2, the account you created when the moodle was installed. But ... see below ..
You've not been successful in restoring any courses? or you have but there are duplicate accounts for what should be student accounts in course backups from old server. If latter, delete courses.
So site would have only 2 users (guest/first admin) and no courses.
Then take one of your backups from old site - if they do not have 'nu' in the filename of the backup, they should include users. Pick the largest backup file first ... tweaks may be needed to php and possibly to mysql ... php time for a script to run ... memory a script can consume (php info in site admin menu) + in mysql max_allowed_packets - backups do have large chunks of data - such as in question bank (quizzes).
In those courses, your new admin account should not exist or there will be a conflict. Moodle protects that admin level account.
Get that largest course backup restored and checked, then the rest should restore without issues.
Exception to what I've said ... plugins ... if you've used addons in old site, install compat versions in new site *before* restoring courses that used them.
Don't worry, at first, about theme ... don't immediately install new theme ... focus on getting courses restored first and site functioning properly before working on the 'fluff' ... ie, how it looks.
Now I know you don't want any 'virtual finger wags' but do make notes of your mistakes in this adventure and internalize them ... and do know that the version you are running will not be 'forever' ... you will have to upgrade the site ... which really is much easier if you do that when versions are closer.
Again ... my 2 cents.
'SoS', Ken