I've had such a bad experience with this hosting company that I can not but share it with everybody so it doesn't happen to other people.
You can see the whole account of what happened here:
On how CWIHosting screwed my sites for a week

In brief: CWIHosting just kicked me out one nice day without any previous warning, and then they held my data from me so I could not move to another hosting company (I made the mistake to keep my database backups in the server). Instead, they proposed that I pay 8 times more to get a dedicated server with them, as the only way for me to get access to my data (and even to my e-mail messages!).

This is definitely not a professional behaviour and can render your site anavailable for well over 4 days! and cause you a lot of trouble and desperation. So my advice is: do not hire any services from CWIHosting.com

I would suggest that you read the TOS for your future host and go for a provider that has a customer support line.

Did you find the cause of the heavy traffic to your site? Did you get your log files finaly?

Yes, finally, after 10 days I did receive the web logs.

I wouldn't expect any TOS to reserve the right to prevent you to access your own data! If only to be able to migrate to another host (as they would not allow me to fix the problem that they claimed my account was causing, and of which I have no evidence).
Isn't that even illegal? Does anyone know if I can start legal action against them?

You are free to start a legal action even if the company has a good TOS, however the end result may not be worth the time & money. They may use the argument that you or your site have violatd their policy and that they are not liable for your site's data - in other words you are responsible to keep a backup of all of your data.

You are right, it's probably not worth it.
Though they never claimed they had deleted my data. They just delayed in returning it to me.