One cabinet?!? Yes you can do it yourself. I would'nt even ask a pro to do it.
Doing it soley yourself would be tricky without holding the cabinet up and screwing. If you can stack something up under it for support and just lay the cabinet on there, you may be fine. I agree with the previous "get a Studfinder" comments because they are very useful and can be used for a lot more future projcets. Any house could benefit with one in it.
Just a little guideline... you already may know that studs are generally 16 inches apart, so when you find the first one, you'll know the approximate distance to the other ones.
Marking the level is key. You can do all the measuring and marking first and finding the studs(beams) and marking them AND STARTING the screws into the cabinet itself while it's still sitting on the floor. All you need to do is hold it in place and finish screwing them in, after that.
A common problem with kitchen cabinets is the walls are not perfectly straight to begin with, but in your case you don't need to worry about that since it's one cabinet and the rest of them are installed already. If it was the whole kitchen, then you'd have to shim the cabinets from the back so they all line up evenly and straight when viewed from the front. Again, it's not your concern on this project. Good luck.
Did you ever do anything with the front porch? I know you had problems getting people out there to even look at it.