Upgrade to 3.4.1 Stuck at Database Update Required

The blog pages still show up on the site OK, but I can’t get to the Dashboard any more. WordPress seems stuck in the upgrade. I get a WordPress page with a button saying ‘Database Update Required’ and when I press it I get one of two results. Either ‘connection to the server has been reset, try again’ or just a blank page with the WordPress logo in a box (same page as the Database Update Required button page, but with no text or button). I’m using Firefox browser, although the results are the same with the MSIE-within-Firefox browser too.

I have tried:
– replacing wp-admin and wp-includes folders with the latest version;
– deactivating all plugins by renaming the plugins folder (there is no mu-plugins folder AFAICT);
– checking the database tables with PHPMyAdmin – I haven’t tried repairing them as the check tables function suggests they are OK. I did download an SQL export of them for now;
– renaming all themes except twentyeleven.

All the above give exactly the same result as above.

Just at the moment I am not 100% sure I’ve accessed the correct SQL database as my notes show a MySQL5 database that I haven’t got into yet… I don’t have time to check right now as I have to go to work. Thought I’d post in case anyone has seen this problem anyway and has the answer.