Question : Problem: HP software won't recognize a connected and working computer and shuts down

I am running Windows Vista and I am unable to get HP Solutions Center to open. I recently installed drivers and software for an H-P OfficeJet Pro L7580 all-in-one printer. The printer work fine as a printer, but am unable to scan and it won't "see" my CPU which is connected BOTH with a network and a USB connection per the H-P installation manual.  If I need to disconect one to fix it, OK, but I need the network connection.

When launching HP Solution Center, a small grey screeen opens, followed by this error message: "No HP devices have been detected. HP Solution Center will close now." when I click "OK", it does in fact close.  HP Solution Center will fail to detect the printer even while IT IS ACTUALLY PRINTING A DOCUMENT!

HP tech support is absolutely useless.. Six calls of over an hour each and nobody has a clue what to do.

Any thoughts anyone - let me know how to fix it and I'll buy you dinner!  Thanks!

Answer : Problem: HP software won't recognize a connected and working computer and shuts down

Correct that - I assumed you were using the XP firewall.
If that's not the case, and for anyone else coming to this page, this is the full list of firewalls and their related steps for opening those ports:
http://h20000.www2.hp.com/bizsupport/TechSupport/SupportTaskIndex.jsp?lang=en&cc=us&taskId=115&prodSeriesId=3601422&prodTypeId=18972&supportTaskId=23044