I sympathise with your present predicament over income, but let's look at the facts.
The Heart Internet terms regarding non-payment for services are very clearly set out. This is the relevant clause:-
"Time for payment shall be of the essence. No payment shall be deemed to have been received until we have received cleared funds. If your chosen method of payment is not authorised by your credit card provider or bank, you hereby authorise us to seek payment from any other credit card, debit card or direct debit registered against your account. Further, if your payment is still not authorised we may, at our discretion, suspend or terminate any Services we provide to you from time to time, even if payment in respect of such Services is not outstanding."
From which you will see that the company was perfectly within its rights to terminate your server access - you failed to pay what you owed.
With regard to the data you had residing on the company's servers, the terms are also very clearly laid out:-
"It is your responsibility to maintain appropriate and up-to-date back-up copies of any data, information or other material you upload (or permit to be uploaded) onto our servers ("Material") as part of your use of the Hosting Services. In the event of loss of or damage to your Material, you will not be given access to the server back-up we maintain pursuant to our archiving procedure."
From which you will see that again the company is within its rights. In any event, it is surely good working practice to keep local backups of all material uploaded to a web host's servers - you could have protected yourself by doing this.
I can't comment on the allegations you make about previous disputes with Heart Internet, but I have contacted them to offer them a right of reply here, in our forum. In all honesty I doubt that they will wish to discuss an individual customer dispute in a public web forum.
With regard to your comments about theft and the police - this is a matter for your own judgement. My personal advice is that no theft has occurred, and that the police will advice you they can't become involved in disputes of a commercial nature where there is no evidence that a crime has been committed. By your own admission you have breached the contract you entered into with Heart Internet, and the company is under no obligation to continue to provide you with a service.