I am trying to install version 2.4.3 on a Joomla 1.5 site and I am getting this error message.

Component Install: DB function failed with error number 1136
Column count doesn't match value count at row 1 SQL=INSERT INTO jos_components VALUES( 0, 'Responsivizer', 'option=com_responsivizer', 0, 0, 'option=com_responsivizer', 'Responsivizer', 'com_responsivizer', 0, 'components/com_responsivizer/images/responsivizer-16x16.png', 0, '', 1 )
SQL =
INSERT INTO jos_components VALUES( 0, 'Responsivizer', 'option=com_responsivizer', 0, 0, 'option=com_responsivizer', 'Responsivizer', 'com_responsivizer', 0, 'components/com_responsivizer/images/responsivizer-16x16.png', 0, '', 1 )

but it also give a success message
Install Component Success

It look like the table 'jos_components' has 14 columns whereas the SQL only has 13 values, and I'm not sure if they are in the correct order either.

This is not an issue of the component, it looks like an issue of your J1.5 installation.

Ensure that the #__components core table has not been altered, i send you the screenshot of the #__components table of the old J1.5 for your reference. It must have 13 columns, obviously if it has been altered you won't be able to install components.

Thanks for the screenshot. It looks like something added another column to mine, well to the site I am trying to update for a customer. I added a screen shot of the table I am working with. I was told this was a 1.5 site and I tried to install the component for later versions of Joomla and they all displayed an error that they couldn't find an xml file, so I am pretty sure this is a 1.5 site. And this was supposed to be an easy job to do... ugh!

Indeed only Joomla 1.5 had the table named #__components, so yes you have J1.5 installation. But the core table has been altered so as a result it won't work anymore when installing extensions, i suggest you to try to remove that extra column restoring everything as by default if possible.