Why will Panels not upgrade?
For some reason that table was never created in the database (this site started on an early version of 7, so perhap the Panels module didn't use a cache table back then???).  You can fix this by creating one that's identical to all the other cache_* tables:

CREATE TABLE `newco`.`cache_panels` (
  `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 'Panels cache, manually created because Panels module would not upgrade without it'


Then you should be able to successfully upgrade the panels module:

$ drush up panels