I am giving credit for the answer to Mafuba because his suggestion is ultimately correct. I am adding my own answer here, though, to provide details in case other folks may not be as familiar with what he suggested ( which included me :-) along with my own suggestions for getting the best result.
Caveat #1: Before you do anything, backup the registry settings for Outlook so you can start again if you need to! This microsoft forum post (Outlook wont run up, mail control panel applet says I have run out of resources) identified the registry path: HKEY_CURRENT_USER\Software\Microsoft\Windows NT\CurrentVersion\Windows Messaging Subsystem
Caveat #2: Before you delete a profile make sure you write down its details so you can apply them to a new one! Open the Mail control panel, select profiles, then examine the settings for such things as your email address, your exchange server, your data file locations, and so forth. When you create a new profile Outlook can automagically determine all of these... except when it cannot (see below).
Issues I ran into:
Could not open the Mail control panel; received the error
"Your system needs more memory or system resources. Close some windows and try again."
Thinking that since I was having an issue with doing something with Outlook the second time, I thought that if I tried the control panel right after a fresh boot, it might open, and it did!
At one point I then began to create a new profile using the Auto Account Setup process but quickly ran into this error
"An unknown error occurred, error code: 0x80070057". The workarounds for that, according to this microsoft forum post Error 0x80070057 occurs when you create an Outlook 2010 profile by using the Auto Account Setup process for an Exchange 2003 mailbox, included doing it manually--which is why I suggested recording the settings from the old profile above.
But since the automatic setup did not work, I decided to try one more thing before creating a new profile manually: in the mail control panel I just made a copy of my suspect profile, thinking the copy process might be cleansing as is often the case. Turns out this worked fine. When I started Outlook, it prompted me for which of the two profiles I wanted to use. I selected my new, copied profile and it opened fine. I closed Outlook and re-opened it and it again opened fine! Also, I could still open the mail control panel; no more errors there. My final step, then was to delete the corrupt profile, and finally do a reboot. Then a couple more checks to make sure I could open and re-open both Outlook and the mail control panel showed everything was now working the way it should.
To sum up:
I would amend Mafuba's suggestion just a bit: rather than delete your profile then recreate a new one, I would try to copy it first. If copying does not work, I would do a create-then-delete rather than a delete-then-create, just in case you need to get some information from it.