I went to your home page and clicked on one of the links from the front page:
Did you change your permalink structure at all or do any other config changes? Because doing a search for the letter "a", I could find your post content but clicking on the URLs are led to error messages.
Give this a read:
Moving your domain without changing the Home and Site URLs of your WordPress site is very simple, and in most cases can be done by moving the files.
Moving a website is not that hard, but it can be a little scary if you are not used to it. It is just files on a server that can be downloaded using FTP or, if you have a decent control panel, compressed into one archive and downloaded to your computer then re-uploaded to another server. phpMyAdmin is the database tool frequently used to export databases. Same thing, export your databases, download them to your computer, then upload them to the new server.
It's a pretty easy process. The trouble spots come in creating a new database(s) at the new host and updating the Wordpress config file if the database user name or password changes. Another complication can arise with plugins as some of them may store file paths or URLs in the database that may change when moving to another server.
I would advise you not to delete anything from your old host until you are set up at your new host. Do not delete any files or databases. Then see this:
Note: if your current host is a cPanel host, the easiest thing to do is to allow one of our talented Tech Support Ninja's take care of it for you. Just open a ticket and they'll get it moved over for you.
I think your old host was using cPanel, right? If you deleted anything from your old host, you will not be able to take advantage of that. However, it is important for you to learn how to do this so you should probably take a stab at doing it yourself (if you are willing).
How many sites do you have to move? Because you are using plugins which may (or may not) store file path information in the database that can change on a new server. So I would advise to move each site one-by-one. And before you prepare to move the site from your old host, disable all plugins first, then download the files and export the database. You can re-enable plugins when you get everything uploaded and imported at the new host.
You may also want to take a look at this Wordpress migration plugin. I have never used it, but the reviews of it are all positive.
To use that, it looks like you: install it at old host and download an archive of your Wordpress site. Then on your new host, you would do a fresh install of Wordpress, install that plugin into your fresh install, then run the plugin to import the archive of your old site. It may be worth a few minutes for you to look at it.
Always keep backup copies of your websites. When you get everything set up at your new host, spend three or four minutes making backups of everything. Compress your public_html folder using the cPanel File Manager and then go into phpMyAdmin to export all your databases (you should be able to do this all at one time), and download them to your computer. Then also make another copy of that backup copy.
Years ago I lost many hours of work when my hard drive failed. Now I make lots of backups. For my most critical stuff, I have the copy on the web server, the copy on the hard drive, and copies on two thumb drives and two external hard drives.