Need to obtain key code to obtain extra key

You can buy it on ebay much cheaper but the dealer has to program to your car. Replacement for Cadillac Chevy GMC Hummer Saturn Remote Car Key Fob Pair

Also fits your Chevy.

dealer only

There is no feature to remotely find the key fob from the car like a tv discovering a smart remote. If you have misplaced the fob with no real ability to recover it, you will have to purchase a new unit at a GM dealer. Most dealers can program the fob to your car as well. Hopefully this helps.

Should be no connection between the two. Those vehicles are always having problems with the radio units in them. You will either have toi get the radio fixed or find a used one at the wrecking yard but then will have to go to the dealer to get the security code done to make it work or get a after market unit. I would say go to a after market unit.

How to Program a Key FOB for the Chevy ' eHow.com

www.ehow.com/how_7508133_program-key-fob-chevy.html

How to Program a Key FOB for the Chevy ... your Chevy, if you obtain new or replacement keys they will need programming to work with ... How Do I Program MyKey Fob? ...

1) Your key fob could need a new battery.
2) Your fuses could need checking.

Go to this website for a new key fob. http://www.keyless-remotes.com/Categories.bok?category=Remotes:Chevrolet:2005:Equinox

Need to go to the dealer for a new FOB to be activated. You can only reactivate original Key FOBS that have received new batteries.

have a locksmith repair the ignition system and programme new keys

WOW I think someone is very confused here.
The key fob & radio do not have anything in common. The first thing I would do is go to your local Chevy dealership parts department and give them the complete vehicle identification number. He can look up your vehicle to see if GM build you car with GM factory keyless entry system. If GM buiilt you car with keyless entry you'll need to have the service department program the key fob to the car. (This is not done through the radio, I've work for GM for 30 years, this is not how they built it)
If your radio needs to programed, that is done through the radio. 2 seperate circuits.
Maybe you should look at going to another Chevy store, I don't think the first one the advisor new what he was talking about.