Probably not the right thread, but since you asked and I saw it: Sure, changing hosts "could" affect rankings, but so could "deleting a lot of your links", and "redoing you website". There's also a 4th potential culprit and that is your rankings changed due to nothing you did.
Back to the hosts: the host could be known for harboring spammers and condoning spam, and have many of their IP's blacklisted. They could have put you on a server (IP) that has a lot of scammers or spammers on it, and it's guilt by association. Check your IP address
here under the "Spam Blacklist Check" to see if it's blacklisted (at least with the places it lists), and put your IP in
here to check out the other sites on your server. (That website is down right now for me).