There is no automatic method of cancelling your account. You have to call the tech support line at https://secure.logmein.com/con... for your locale. All you can do on the site is delete the computers on your account. As of this post, I cannot get through to the US & Canada line, just getting a busy signal. Apparently I'm not the only one following this route. As has been mentioned in other posts there are plenty of free options out there capable of the same features that a free LogMeIn account was capable of doing.
I think you mean 3% of the Federal budget, not GDP. See http://www.richardb.us/nasa.html. In which case, for the years 1962-1972, NASA's budget was 2.86% of the Federal budget.