If your tap water is fluoridated, it might help to switch to drinking non-fluoridated water. I started drinking non-fluoridated water about a year and a half ago, and since then I've been able to sleep better and think more clearly. Here's a link with information about neurotoxicity of fluoridation: http://www.nofluoride.com/mullenix_bsa.cfm
Give yourself little rewards for doing little tasks. You can plan to play with a toy for half a minute, physically pat yourself on the back, stand up, put your arms in the air and turn around, etc. Practice congratulating yourself and feeling good about getting small steps done.
Lucy Palladino's book "Find Your Focus Zone" has some good techniques. I particularly liked how she pointed out that for each task, there's an ideal level of adrenaline (not too high, not too low), and that you can be aware of your current level of adrenaline and what the ideal level is for the task you want to do right now, and use specific techniques (like taking some deep breaths, walking around for a minute etc.) to raise or lower your adrenaline to just the right level.
Being most productive the last couple of hours of the day because there's a deadline suggests that earlier in the day at least, raising the adrenaline level would help. A good exercise workout before work in the morning and/or at lunchtime can raise dopamine, helping you concentrate better for several hours.
You can set deadlines for yourself: e.g. choose a small task, set a timer and decide you'll see if you can finish the task before the timer goes off. That's a way to make work more fun and raise adrenaline. You might try the Pomodoro technique.
Saying things aloud, even if you're just talking to yourself, can also help raise your alertness level. "Now I'm going to ...[small step]"
You might like books like "Time Management for Unmagageable People" by Anne McGee-Cooper and "Time Management for the Creative Person" by Lee Silber.
Inability is an abstract thing involving comparison with alternate universes; it cannot be experienced.