I thought that you can cancel anyway but that you will have to pay the full amount for the period you used the service.

Actually that aspect doesn't really matter.
I think by law they are required to accept the premature cancelation of a contract, without fees, if the service provided is not up to par.

In cases like mine, the 4G internet connection that's supposed to be provided, is almost non-existent. It's not my fault.

If they want to penalize me with 400CHF for the cancelation, I will refuse to pay and contact the Ombudscom.

FYI, I had a somewhat similar situation with Salt a year ago. They made a special time limited offer that I registered to take. I don't know why but as a precaution I decided to take a screen shot of the offer and my registration.
When I hit the enter key to process there was a hang up in registration and it seemed like it did not go through. I called customer service and they said the offer was no longer available and I would need to pay a higher rate.
Lucky for me I could send them the screen shot images and I was able to get the preferred rate in the end.
I all seemed a little deceptive so the lesson learned is to always take a screen shot of special offers when I process them online because there is no paperwork.

I had a bad experience with Sunrise today.

I'm moving a mobile number to UPC, and got notified of a transfer date at the end of January. Which is a PITA as it's the day before our ski holiday.

Checked my contract and found that the notice period is one month to the end of the month, so I called them up and complained.

Helpdesk told me that notice period is 60 days to the end of the month, which I told them was nonsense as I'd had no notification that I was aware of. They told me "you definitely got notification on your bill, and the details on our website".

So, checked all my bills, no notification.
Checked website, document actually says "60 days", no mention of end-of-month.

Phoned them back and complained again, made it clear that changing contracts without notification was bad enough, but just making shit up to get rid of me was not acceptable.

After much back and forth, finally ended up with the 60 days to mid-January since they could hardly deny the T&C which are currently on their own website.

And immediately cancelled two other Sunrise contracts. Shysters.