Not able to login to wp-admin – error in header

A client who runs a wordpress blog updated their wordpress version and now has the following error in the header:

Warning: Missing argument 2 for wp_widget() in /users3/domains/insidepocket.co.uk/web/blog/wp-includes/widgets.php on line 76

They also no longer are able to log in at wp-admin. The following error appears:

Warning: Missing argument 2 for wp_widget() in /users3/domains/insidepocket.co.uk/web/blog/wp-includes/widgets.php on line 76

Warning: Cannot modify header information – headers already sent by (output started at /users3/domains/insidepocket.co.uk/web/blog/wp-includes/widgets.php:76) in /users3/domains/insidepocket.co.uk/web/blog/wp-includes/pluggable.php on line 897

I said I’d sort this out for them but as I can’t log in the only option I see is a clean install of their blog. Is there a way I can prevent losing all their posts (as they didn’t have a backup either…

Thanks for your help!