The point is not being productive, but looking busy. Honestly, if the OP had the option, he should take a 2 hour nap, a shower a late brunch and start working about noon. If he cannot, it is probably because he has to be there at the office.

So, how do you waste the day in the least damaging way? I think the key issue is - Find chores you can do with minimum thinking. When I have been in this situation (yes, yes... I should have not... been there, done that) I found myself unable to make anything creative, but still pretty able to knock off tasks that I had previously planned and prioritized. Write those emails you were planning (and triple read them, don't want to embarrass yourself or offend anyone), perform that refactoring you had identified but you were much in a hurry to actually code, start filling the TPS reports due next Friday.

Also, you might want to take a 20 minute nap after lunch. You will still feel crappy, but it will boost your attention span for the rest of the afternoon.

And please avoid driving altogether!

You may be _more_ productive by going to sleep. That way you won't be forced to fix all the bugs and crazy decisions you make while you're sleep deprived.