Ok, If the broken part of the key is not stuck in the ignition, this is what you need to do.
Firstly if the remote buttons aren't working anymore then the remote won't need programming, it just has a flat battery which is replaceable. The remote (buttons) section of the key can be removed and fitted to the new key. If you have a jewelers screwdriver set then you can remove the remote yourself, then unscrew the remote cover, pop the battery out and then your local electronics store or even your local pharmacy will have a replacement battery for you. Just match it up with the numbers on the battery.

You need to have the key cut (copied) by any major locksmith or key cutting service. If you have a major shopping centre close by then check if they have a Mr. Minit store there as they can cut the key and also replace the battery for you.

Don't forget that if you have any more questions or you are unsure of what I mean in the information provided please ask for more clarification, I'm only too happy to work with you to achieve a good result. Remember even after clicking 'accept' we can continue the current conversation without further payment. Cheers Glenn.