Can you download a exact copy of your website and then virus scan it to make sure that while at the web host it didnt receive any tag along scripts? If the host was hacked malicious code could have been added to your sites content. Its a far fetched idea that your host could have been hacked and malicious coded/script added to your content, but I have seen sites before that have had nasty scripts planted by hackers. I found them mostly when making offline copies of websites with httrack. I download all the guts of a specific site and then next scheduled virus scan a file is flagged as malicious and the site that I made an exact copy of for offline use had a bad script on it that likely wasnt put there by the webmaster of the website.
Are you moving from a free web host to another to where the free web host might have questionable in ethics with offshore immunity?
The site your trying to move it to might be detecting a real problem vs a false positive I feel. Otherwise if its a false positive figure out why and correct that problem.
About 10 years ago I hosted my own website with my own web server a Windows 2000 Professional computer with Apache installed and a software firewall, and an exploit in RealVNC allowed for a hacker to get in and add content to my web server to host their own stuff on my server. I killed that off as quickly as I found it. I didnt even look at the contents, when my internet connection got slow I went looking and saw tons of activity from my web server. When looking at the packets with wireshark on my other system on same network, I saw odd traffic and when visiting my local web server to see what was going on i found all sorts of folders and files that I did not dare open and killed the power switch and wiped the system clean as for I had an image of my web server and my websites most recent version was on my other computer to bring my web server back up and running and disable RealVNC to get rid of that exploit, but to later use that exploit as a honeypot to bait hackers when i no longer used this system as a web server.
I switched from Windows 2000 Professional to Fedora Core 5 Linux for my web server which was more secure. Then shut off my website when i no longer had the satisfaction of running it.