For whatever reason, Linksys's 877-959-7467 phone number doesn't appear to work at all. The company seems to have disconnected this number for customer service but hasn't told all of its affiliates.
That theory is because when searching this number, you do get a Linksys website, but it's the British version of the site. When visiting the website, you're asked if you would like to go to the American version of the website, which lists a completely different set of phone numbers on its support page. The American website offers three different phone numbers for customer service, but none of them are this number.
That's because calling this phone number yields nothing at all. When I dialed, I got a failed call tone and a message that the call could not be completed to this number and to "please hang up, check the number and try your call again." I tried the number two more times, double-checking both times to make sure I had entered it properly. Again, I had no success getting the phone number to work.
A further search shows that this number is also listed on the French website under American support numbers. You need to translate the page from French to read it, and after doing so, it reveals that this number used to be for customers who needed help buying online. It's not clear when Linksys decided to either fold this number entirely or amalgamate it into its other forms of customer service, but it's clear that the company now treats customers who want to buy online the same way it does those who need technical support.
Unfortunately, because of the lack of updates on the European websites, it's still very possible for someone to waste their time trying this number. That's even more true given that one of the sites with the erroneous number is the British website, which doesn't need to be translated into English. The British site is also the first one on the page, so it's easier than Linksys probably assumes to find this incorrect number. If someone is strictly searching through Linksys' American website, it will never find this number there, but ex-pats living abroad might run into this number while trying to find assistance.
As such, there isn't any reason at all to use this number. You can't get connected to anyone at Linksys, you can't interact with the number at all and you can't even get a correct number to contact someone who can actually help you. There's no benefit whatsoever to calling this number.