My advice is to make sure you've backed up everything on your computer 1st. Once you've done that, just setup a fresh Wordpress.org install, then re-upload all the FTP files from the old website install.
There's a possibility you may need to go into your FTP files and make a couple manual changes through the code edit. Try doing the basic things first like pointing your DNS to your new hosting account, etc. Tag my profile & let me know if you need more help.