There is no immediate termination - first time you can terminate the contract is to the end of the contractual term - usually after 24 months. So if you send a cancellation, it'll be processed exactly the way you signed the contract.
Next thing: If the internet doesn't work immediately, you can just request a technician to set up the line - why do you need an immediate cancellation instead?
And just to be precise: There is no right to cancel immediately - not even within the first 14 days. A cancellation request will become effective to the end of the minimum term - and nothing else.
Anyhow you might be confusing this with the withdrawal period - but this is not a general right for all contracts but only applies to contracts made using telecommunications means -or- contracts made outside of the regular store or office rooms (e.g. on special events -or- if somebody comes to your home). But the thing is that if you write "Kündigung" / Cancellation, than this is a completely different thing than if you write "Widerruf" / Withdrawal.
