right there are 3 ways to sort it,
1 the cheap route, change the barrel and always have the blue part of the key next to ignition so immobalizer can read the chip from your (snapped)key,
2 more expensive, change all your locks and barrel and get the keys reprogrammed to your cars immobalizer, (you will need your old red key to do this)
3 take out your barrel and take it to a specialist and get them to remove the snapped key,
last thing if you need to use car asap ya can always take cap of rear of barrel and use a screwdriver (but i neva said that lol) again leave the snapped part of key near barrel,