Windows Not Updating Correctly

Exploit:Java/CVE-2010-0840.DT is from April of 2010 although it was reported to Oracle in November of 2009.
If the installed Java runtime had been kept up to date and your User Account had been a Standard User, then nothing would have occurred.

Apparently, something did occur as your User Account's type was changed to Other - Debugging User, the system was having difficulties updating, and MSE was very slow to update it's definitions.

If I were your IT guy I'd either restore an image or do a scan with a Linux-based virus rescue disk so that the system can be Trusted.

You previously posted

Other work stations in the office have their user accounts set up as administrators, it's just how it's set up here. If it's best that we aren't set up as administrators, maybe it's something that I need to notify him of so he can get that changed on all the other user accounts in the office.

Unlike Windows XP, Windows 7 was designed so that running as a Standard User does not require all sorts of manipulation to run software and for day to day use of the computer.
Please show the IT Guy that article I linked you to in my previous post - Report: 64% of all Microsoft vulnerabilities for 2009 mitigated by Least Privilege accounts