Error 403 and site not loading

I have been posting blogs on my sites.  By the 9th blog I was unable to post.  Got message saying error 403 I did not have access to this part of the server.

I have 2 Boonex sites.  The other site consistently times out on my home computer.  All was woking fine before.  Also just before this I got a few fake members on both sites.  Both sites had lots of low resolution pictures that I deleted along with banning the memberships. 

Does this sound familiar to anyone?  How can I prevent this?  It seems I will have to start from scratch because changing the hosting company has not helped. 

Please advise

First clarify something; do you mean that you had 403 errors for your site and that you decided to move to a new host and that after you moved the site you still got 403 errors?

How did you move your site?