[titchyyyy]

Deal with them over email. Get a picture of the device with the serial number and send it to them. You won't get anywhere without one unless you're really good.

If they're asking you to contact retailer, you have to work your SE magic and tell him that you've already contacted them and they told you you're outside of their warranty and they've advised you to talk to Logitech directly.

SEing is all about how you deal with the company in question. If you give up when they're asking you to contact the retailer, you've failed already.

Keep at it and find ways through it.