To say I can't run is being kind HELP.

you need to be focusing on slow efforts.   Put in lots of volume doing the slower pace and you will see it become easier and easier until your pace starts to pick up and longer distances become easier.  You just need to focus on running lots and running consistant.

I agree with vortmax. I am slow too. I've never been fast even as a kid. when I first started this tri stuff last summer, I could barely run a mile with out gasping for air.

BUT, recently, after doing LOTS of running at the 10-11 min mile, I actually raced at like 9.5! For me that was HUGE! And it gets better all the time. I just worked on slow speed which was easy for me but I didn't push push push like I had been and thus getting winded and discouraged. Just worked at 'my level' but kept adding little bits of distance. I don't always work at speed either... I work on distance too and ALL the time mindful of form and keeping myself injury free. (had achilles issues last summer too).

It will come...hang in there!

My running has slowly improved over the last 4 years.

One thing to consider not yet mentioned is technique..most folks just go out and run and think we did it as kids so I know what I'm doing. Technique matters in running like it does in swimming. Have your evalulated and see if you need to change anything.

I changed how I ran and dropped 45" per mile off my run time.

Consistent running all year 3x a week really helped and yep not running to fast, but training my your heart rate is key.

I do this 4 mile loop back starting in July 2004 now I run it in 2/3 the time it took me 3 years ago. Patience for improvement and smart training is key and for some of us it just takes time

A general rule to avoid injury is to not start speedwork until you are running 20-25 miles per week.   Also the expression "recovery run" should make sense to you before attempting speedwork

Run more, run long, run short, run every day, run twice a day all slow and easy.  Many running adaptations take years to develope. 

x2.

Lots of volume will help immensely. I went from a 15:00 minute mile (walk run combo) to a 10:15 min mile in about 9 months with nothing but volume, no speedwork. Though I did train with a HR monitor during that time to make sure I was in the proper zone (zone 2) during my long runs.

Incidently I could never get a long run in zone 1. Zone 1 was walking. Here I am, a year later, and I can do a 2 hour zone 1 run at just under 12 m/mile. Keep it up!

I'm surprised that no one has suggested running more.

HRM training at 70% Heart Rate Range or even just 70% of max is great for making sure that easy/recovery runs are really easy and not taxing on your body. I've put in painfully slow runs, hardly breaking a sweat, but it's helped me run more pain-free and let me run faster when I want to. Like everyone else said, put in the time on the road, and you will see improvements.

Now, if only this could hold true for swimming... 

That's impressive Kathy!  What method do you use if any? (Chi running, evolution etc.) 

Run more often and run long.  Anything less will give you little to no results.

Hint: 6 miles is not long. 10 miles is getting there. 15 miles is acceptable. 

that is a little excessive to start with.  I would find a training plan and pick a target distance.  Work towards small goals.  The most important thing is to run frequently and consistantly.  Running 2 miles, 5 days a week will do more good then doing one ten mile day, once a week.  Don't even think about (real) speed work until you have picked an A race, have run the distance, and know what kind of time you are trying to hit.

One thing that worked really well for me when I first started was to target one distance.  I said I wanted to be able to run a strong 3 miles.  So I focused on that distance.  I would run 3 miles three days a week, and on the 4th day (on the weekend) do 4 or 5.  I kept this up until that three mile run was a cake walk and my pace started to increase.  Then I moved on to 5 miles.  I could already run that distance from the longer run on the weekends, so I consistantly ran that distance until 5 miles felt like a relaxing jog in the park.  Basically following this method, I hit the point where 10 miles was no problem and was quite an enjoyable run.  Also, the more comfortable you become with a distance, the faster you can run it.  Once the distance becomes 'easy', start to push the tempo just enough to make it no so easy any more.

Just remember to have a rest week with low volume and low intensity after evey 3 weeks of training.  It's 3 on, 1 off.  Also once you get to the 5 mile mark, I would look into an actual training plan that makes better use of the 3 build weeks and 1 rest week.

As a new runner, I'd run 3 times a week and only build up gradually following 10% rule. You need to stay healthy, allow your body to adjust to running and adapt, and be able to be consistant.

Someone asked how I changed my running and improved ...my tri coach taught me to forefoot land from being a previous heal striker which I didn't know I was doing. Newton running shoes help with that too. I bought a pair and really love them...their design helps your body adjust to landing like that due to how they are made.

15 miles as a long run once per week is the goal.. not 15 per day. Sorry I wasn't clear.

I would run 3 minimum, 4 (optimum) times per week to start and do the increase by 10% rule ,mentioned above. 1 long run, 1 tempo run, one mid distance run of 6 to 8 miles (once you are up there), and maybe an extra 3 miler in there somewhere. You will be where you want to be in no time. Use recovery weeks (step back weeks) and be patient. Just remember, the goal is get the volume up, injury free. Once you get there, don't let it slip. Make it a habit. A strong running base is like the foundation of a house in that it's what everything else is built on.