Moving WP

I had a web site setup on one host as a subdomain and I had to move it, so I backed up all of the folders to my local computer. I then deleted all of the files from the host system. As I had created the website under MYWEB, I thought I could just load the MYWEB folder up on the new host and all would be fine.
I would like to just get the pages I had created. I have a new version working, but If I could open the old pages on my computer or some where and copy the content in to the new MYWEB it would save so much time!