Another thumbs up for the Couch to 5K programme. Tried and tested by loads of people just like you. One thing I'd recommend is that you get yourself fitted for a decent pair of running shoes - go to a proper running shop, not to the internet, or sports-goods warehouses, where they know almost nothing! The wrong shoes can lead to injury, and that will put you off. And if you think they're expensive, then just think that your new lifestyle might easily be saving you a tenner a week - that's only a couple of 'coffee & cake' stops and a packet of biscuits!
Depending on how you feel, you could look to find a friend to team up with - to run with - to diet with. If none of your friends do... then see if there's a running club in your area that caters for beginners... a great many do, and you could team up with someone there. Personally, I've been happy to run alone... but loads of people benefit from a buddy.
You're right in knowing that running doesn't, in itself, deliver significant weight loss. Certainly not until you're running some distances longer than 5K... but it contributes a great sense of well-being... and a motivation that, if your willpower crumbles in the face of that little piece of cake, it's the equivalent of running an extra two miles. It kind of puts it in perspective !
Try and make it work this time... but if it doesn't... then don't criticise yourself. Sometimes you need to make the resolution 4 or 5 times before eventually it clicks. Good luck.
Edited: 30/10/2012 at 12:53