I am not a runner either...I mean as a kid I played tennis and sports like that...but never did track or jogged. Now that I am training for a triathlon, you need to be good at pretty much everything. I bought a new pair of shoes at a running store where they put you on the treadmill and examine your ankles to determine how you pronate. They will tell you what type of shoes you need to put your foot in the correct alignment. THIS is what will get rid of your shin splints...having the proper pair of running-only shoes. So don't give up on the running. Also, I bought the Nike+ system that you can use to log your runs and determine your pace. The stats show that if you can complete 5 runs, you will continue to run. It works with your iPod and automatically uploads runs to nikeplus.com where you can see your progress.
The biking...you should probably take a look at some new equipment. The technology has changed dramatically in the last couple of years. Instead of throwing all of your money into upgrades, look for a used carbon bike that is a few years old. It will already have everything you need. Pace yourself in the beginning and don't go all out until you are ready. Also, mix it up a bit, some days long and slow, others short and quick. Pretty soon you will be having an easier time with it so you don't have to walk home. Increase your distance over time. Also, make sure you have the proper tire pressure.
Better yet, sign up for a Sprint Triathlon. Give yourself about three months to train before hand. I guarantee you that once you sign up, you will train because you want to finish and basically not pass out!
Good Luck,
Brent