Re: botched data post-upgrade
Well, seems to me you've proved beyond reasonable doubt that the new installation is fatally out of integrity, but. if you have the 5.1.59 files, I think the fix is painfully long but ultimately hopeful ...
1, backup the current mess just in case
2, delete the mysql installation (_all_ its files)
3, install 5.1.59
4, copy in the 5.1.59 backup
5, regression-test (like the irishwoman who took two pills to be sure, to be sure)
6. do a full mysqldump, eg: mysqldump -uUSR -pPWD -A --add-drop-database -K -E -R >mysql5159.sql
7. Now start the recommended sequence:
a: install 5.5, run mysql_upgrade, import the backup, regression-test, fix issues
b: once everything checks out, do another mysqldump > mysql55.sql
c: repeat a & b for 5.6.