Hi, and welcome to Geeks to Go!
Let's try to figure this out.
If not, create a new mail profile for Outlook. You will need your email account information to accomplish this. Be sure to close Outlook. Make sure the Outlook process is not in Task Manager. Press Ctrl+Alt+Del, Task Manager, Processes, click Image Name (1st column heading) to sort the processes alphabetically. Scroll through and if you see Outlook, highlight it and press "End Process". Click OK to any warning you get.
Click Start, Control Panel, Mail, Show Profiles, check "Prompt For Profile", then click Add. Name the profile, then follow the setup process to recreate one of your email accounts. If this proves successful, we'll add the other account later.
Open Outlook, choosing the new profile you just created, send an email. Confirm that the recipient received it okay. Have that person reply. Did you get one or two?
If this fixed the problem, we can import everything from the old account. Close Outlook and reopen, choosing the old profile name. Be sure you're in Mail or All Folders view. Right click the top folder level (probably Personal Folders or something similar), General tab, Advanced button. Put your cursor in FileName and arrow to the right to see the path and file name that holds your data. Make a note of this file name. The file should end with .pst and the path should be C:\Documents and Settings\username\Local Settings\Application Data\Microsoft\Outlook.
Close Outlook and reopen, choosing the new profile name. Click File, Import/Export, Import from another program or file, browse the list for Personal Folder File (.PST), browse for the file (from the above paragraph), check "Do not import duplicates", Next, check "Include Subfolders" and choose "Import into same folder", open the dropdown and choose "Personal Folders". Confirm that your Contacts, Inbox, Sent, etc., are back.
Now add your other email account back. In Outlook, click the Tools menu, Email Accounts, Add new account.
If creating a new profile didn't fix it, or you had issues with my instructions, please post back.