I don't believe that's a legitimate and responsible reply from your host support, so let's ignore it and move ahead.
Usually, with respect to login issues, forum policy mandates a link to your gallery and a non-admin test account, but I can understand your apprehensiveness due to the circumstances. Still, it will make it that much more difficult for some to provide assistance.
So, let's eliminate some settings that may cause something like this. First, I would update the gallery to the latest version. You didn't indicate your current version and you must. But before updating, FTP into your account (be sure your client is set to show hidden files, if necessary) and search your web space for files called .htaccess (including the "."). If you have any of them (and they may be inside every folder you have from your document root down, FTP them to your desktop, then delete them from your web space.
Next, access phpMyAdmin (you will have to log into your cPanel for this) and find your Coppermine database on the left-side navigation bar. Select and click the CPG database and then select and click cpg_config. If you are using a more recent release of CPG, look to your right for "Page number" and select 4. Scroll down to login_threshold and verify the number -- most use 5. If your number is 0 or 1, change it to 5 or more. If your number was 0, or has no data at all, this could cause your CPG issue, but not your account issue. And I don't see how they could be related unless (a) you were hacked and (b) the hack places .htaccess files within your web space directories.
I don't know that I could assist you any more than this. You can try the steps above, then update you gallery to the latest version.
You should also have a look at this thread:
http://forum.coppermine-gallery.net/index.php/topic,51927.0.htmlYou may have been hacked, and if so, the above will cure you.