cache_form has been truncated. Permanent error MYSQL Incorrect key file when a form is accessed
This sounds like someone tried to do some optimization to {cache_form} through a MySQL interface and did something that makes it incompatible with Drupal, or the table is damaged due to a dull disk (see this happen before).

First make sure you have free disk space, and then do a CHECK TABLE cache_form; and see if there are any errors.  If you see some, you can try the standard repair techniques, but it is often best to just re-create the table.

These steps are dangerous and can destroy your site.  Make sure you have backups.

To re-create {cache_form} I would

Start a MySQL interface , and delete {cache_form}, eg DROP TABLE cache_form;

Recreate the table from a known good Drupal 7 install.  I think this is the default:

CREATE TABLE `cache_form` (
  `cid` varchar(255) NOT NULL DEFAULT '' COMMENT 'Primary Key: Unique cache ID.',
  `data` longblob COMMENT 'A collection of data to cache.',
  `expire` int(11) NOT NULL DEFAULT '0' COMMENT 'A Unix timestamp indicating when the cache entry should expire, or 0 for never.',
  `created` int(11) NOT NULL DEFAULT '0' COMMENT 'A Unix timestamp indicating when the cache entry was created.',
  `serialized` smallint(6) NOT NULL DEFAULT '0' COMMENT 'A flag to indicate whether content is serialized (1) or not (0).',
  PRIMARY KEY (`cid`),
  KEY `expire` (`expire`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8 COMMENT='Cache table for the form system to store recently built...';