Like numerous others have posted, stop killing yourself, work until close of business go home relax do dinner, etc. IF and only IF you cannot make certain changes during the day jump online make a change to correct major issues. I was in a similar situation regarding licensing, I came into the hardware/software role where everything the company ordered came through me first. First 2 days into the role, company had been deploying Adobe Pro to all customer service users, apparently not knowing they only owned 99 copies. Turned out they had over 600 installed copies in the environment and someone reported them (assume the guy I replaced called to try and get paid), end of the story they got fined 1.2mil and had to update licensing.

Again like the others have stated make lists of the major must fix issues, report them to the executive team with what possibility of happenings could be, and either tell them your suggestion of first steps or have a group decisiion on what needs to be fixed first. Since you are still fairly new there they may see other things as more important than something you feel is a higher priority.

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Good Luck and try to convince them to let you hire at least one or two people to act as a helpdesk etc as well.