When I turn on Joomla 1.5 cache, my links deteriorate to

fiberglassics.com/index.php/images/comprofiler/images/comprofiler/plug_profilegallery/3587/images/banners/glassic-forums/templates/fiber7a/css/banners/components/com_kunena/template/200907_the_lips/images/english/media/system/js/components/com_kunena/template/200907_the_pearl_white2_153/components/com_comprofiler/plugin/language/default_language/images/images/banners/images/com_adsmanager/categories/glassic-gallery/category/glassic-forums

instead of www.fiberglassics.com/glassic-forums

also the site breaks and all pages look wierd, like a site map.

I turn it off and it works ok, (slower) due to no caching.

Hello,
this would seem like multiple processes would be attepting to write to the cache file at the same time and break it.
But it is just guess the reason may be also elsewhere. You should check the content of the JoomSEF cache file, if such records is found there.

What OS are you using? Try to check JoomSEF advanced settings and play with the file locking options. This should not occur normally.

Yes, I did check there and actually turned off JoomSEF cache. I thought that having two caches on would be a bad option. It appeared to work for one day and then came back (I had turned Joomla cache back on). Maybe I'm not following the right sequence.

Right now, I have Joomla cache off and JoomSEF cache on (I had cleared it all out before turning them on). My concern is that the site seems to load much slower and a few months ago my ISP made me turn on Joomla cache as it was taxing the shared server.