You have to make sure the database(s), or at least the table(s), on both computers are EXACTLY IDENTICAL. I use my machine at home to program for a remote server, and I used to get errors like that because I'd forget to make the new changes on the server-side database.
Also, sometimes it has something to do with quotes. If you have a query that includes a php variable in it, it might have quotes in it that offset the code. There is an option called magic quotes in the php.ini file that sometimes takes care of that problem for you and maybe the option is turned on for the original computer but not for the other. I don't mess around with magic quotes; I like to use the addSlashes() function. If you're not familiar with any of this, search for it in this site.
If everything is exactly identical and the quotes are not the problem, try to find which mysql result is causing the error and post the query for us to dissect.
Hope this helps.
Rubric