I wouldn't say that my, "entire being opposes the task at hand". I would reserve that sort of language for ethical reservations about a task. I do not do things I consider unethical.

But I do encounter many chores in my work that are boring, that are bad ideas, that are for difficult customers, or often all three. I can have the same problems getting those tasks done, just like you describe. Actually, you seem to be way ahead of me because it took my far to long to figure it out. I thought I was losing my ability to program. I was wondering if I was going to have to find another career because I had lost my ability to concentrate. I was reading books on getting things done, and concentration and trying to figure out what the hell was wrong with me. I would sit down to do a task, check email, check reddit, check hacker news, check reddit, get coffee, go to the bathroom, check reddit, "Arg! I have shit to do!" Check reddit, check IRC, etc. I caught myself more than once closing a browser tab with some distraction, pausing for a half moment to organize what I should actually be doing and then open a browser tab to the same thing again.

The insite came when I finally got something engaging to do, and I just powered through it. I could still program! How did I get in the zone? How do I get there again when I need it? Well I worried about hat for a while, thinking there was some combo of sleep, nutrition, environment and task management software that I could line all up and get back to "the zone". It finally dawned on me that I subconsciously find distractions to avoid doing things I don't want to do. What a revelation.

How do I get over it? Well I still struggle with it, but simply identifying the problem was a huge step towards fixing it. Here are some techniques that I use:

Pomodoro technique. This is a productivity trick that actually works pretty well for me. The short version is that that you make a list of very small tasks, then work for twenty minutes (straight! no phone, no emails, no coffee, no bathroom), then take a five minute break. This helps with distraction problems because you can tell yourself, "I can goof off in 7 minutes". It sounds like a lot of interruptions, but I'm amazed at how much I get done with it.

Creating crisis. I work harder with the Sword of Damocles hanging over me, so I put those swords there myself. Call me back at 2:30 and I will have this done. Then I'm good for two hours of, "oh shit, oh shit, oh shit," type production.

Pair programming (and rubber ducking). This really helps to power through crummy tasks. Unfortunately, I work from home for a tiny company. I don't have anyone to program with. But if I am really stuck, I can ask my wife to sit next to me, while I explain what I am doing, and what I am trying to accomplish, and the details of what I am coding as I code it. I can use this occasionally to get over a hump.

Change of venue. I have struggled to find some shitty bug in some shitty spagetti code for a crappy website selling stupid things for WAY too long. The only way I broke through was to take my computer somewhere else, in front of other people. David Sedaris has a great story about a book suggesting he make a change in his house to help him quit smoking. Buy a new couch or something in order to change the venue. In our comfortable habitual surroundings we act in comfortable habitual ways. So he moved to Japan to stop smoking. I can't do this every day, it's just for breaking major blocks.

Anyway, I need to get back to work. Good luck!