Before you call them about the modem I would contact the shipping company and get any delivery details you can. Get the tracking number, who signed for it, when they signed etc. That will be you evidence that they received it.

I went through the same nonsense with my old ISP. They made it impossible to cancel. After wasting tons of time arguing with them on the phone, I found this link. The advice works for cell phone providers as well.

Consumer advice on closing an ISP account.
www.findanisp.com/consumer03.php

A little tip. When calling a company, get the name, employee I.D. and city the employee is in BEFORE you explain the purpose for your call. Tell them you need it in case your disconnected and need to be able to refer back to the conversation. If you tell them you are calling to cancel, they will give you the runaround and even hang up. At least that has been my experience.

Whenever you have to return something (Modem) to the company, make sure you send it certified/return receipt, otherwise you have no proof that it was returned. You will want to send your cancellation the same way and save a copy for your records and credit card provider.

Here is something I found in a forum. More of the same, different twist.

Glad your new provider is working out for you.

My "cancel" procedures with any third party.

These procedures apply to all types of cancellations. Your ISP, your hosting account, your Newspaper, your Cable TV, and numerous other subscriptions you have.

1. Prepare to take notes before you call or click. This means paper and pen, the full name of the person you spoke to, position, the date and time you called or clicked, and print any forms which are related to your cancel.

2. Conduct yourself in a VERY POLITE manner. Don't use profanity, gutter talk, slang, or other socially repugnant techniques.

3. Expect a sales pitch in an effort to retain you. This is business and no one likes to loose a customer. Even if you hate their guts, try using a simple reason for leaving like, "I no longer require your services" and say no more. Some services like your dedicated server may require written notice as per the contract you signed. Don't fight city hall, just do it and confirm receipt and save your paper work.

4. Get precise with these questions and write it down: Exactly when will my last charge appear on my credit card? What is the effective date of the cancellation? Are their any additional charges? What is my confirmation number?

5. Save all your notes and documentation. Carefully monitor your credit card statements and insure that a new charge for a canceled service does not appear which is contrary to the question and answer you received in Item 4 above. If the vendor continues to bill you, just dispute the charge with your CC provider and don't bother calling your service provider.