Sounds like you like to use a challenge to pursue to find motivation to run. For running a half marathon many people like follow a marathon training plan. This isn't necessary but many people do it because the plan incorporates nice long distance runs once a week and builds up millage to 40 miles/week or more. Runs per week are about 3-4 and as high as 6-7. About 1-3 hard runs a week with 2-4 easy runs.
In other words, many people do alot of training in order to run that distance fast. Since you want to finish in 2 hours and have a hard time doing a few kilometers I think you can achieve it.
Here are a few tips. Walking fast can be just as exhausting as a jog or slow run so keep that up. Dont try to run at a hard effort for any specific distance until you have run that distance for 2-3 weeks and have done at least one run at the distance were the pace has been changed between easy and hard (like intervals, progressive runs, or fast finish runs). Build up a routine that includes a long run for 2-3 hours. Dont jump up to any pace, distance, or time without bulding up for it. Build up to 2 hours for the long run and dont worry about taking walking breaks. Eat and drink water for any run close to 2 hours which includes any breaks. Mentally accepting to take a break at any time can allow you to run farther and faster without taking a break - well at least for me. Dont run hard unless you feel good. Dont bother running for more than 3 hours until you need to do it for meeting a training plan distance during your future marathon training :) Running easy means you can talk, you are not breathing hard, and you actually find yourself paying attention to your surroundings. Running aerobically means your breathing rate has increased noticeably, your conversations are limited to short statements, your moving well but not reaching or pushing too much, and your not feeling your heart beat. Run long runs easy. Build up to 1-2 aerobic medium to hard effort runs to about 15-18 km about 4 weeks before half marathon - at or near goal pace. In the weeks leading up to the half make sure to taper but by reducing your overall distance without slowing down your pace (or speeding it up :)
Hope this helps. A short list of popular coaches and authors that might help through their books and websites are Greg McMillan, Hal Higdon, Jack Daniels, and Pete Pfitzinger. A good source of motivation to get out there and run can be found by seeing what others are doing by checking out running apps for your phone and PC like Endomondo and Strava. Endomondo is popular in Europe and Strava in the US. Strava is great for finding places to run and Endomondo is great for tracking your improving fitness & speed.