Hopefully you haven’t lost it, but that error isn’t a very good sign. However, all is not lost - lets see if we can sort this out.
First of all, lets try to take a backup of the database.
In phpmyadmin, select the database from the list, then click the Export tab. Click ’Select All’ at the top, then make sure that ’Add DROP TABLE / VIEW / PROCEDURE / FUNCTION’ is ticked (in Structure) and ’Save as File’ are ticked (at the bottom). Then click ’Go’. Hopefully this will download a .sql file which is a database backup. This file can be restored into a new MySQL database locally to test it out. Instructions for doing this are available on my site here:
http://www.codeistry.com/help/uploading-downloading-and-backing-up-modx-sites
Next thing to do would be to attempt to repair the offending tables. If you click on the Structure tab at the top of phpmyadmin, then tick the tables you want to repair, there’s a dropdown list at the very bottom called ’With selected:’ - pick repair from this list and see what happens. Just do one table at a time, starting with the smallest *_log table and let us know what happens.
If they repair successfully, do another backup, then try logging into MODx manager again.
Just out of interest, how many records does phpmyadmin say there are in your *_log tables?