Go to Start | Run | msconfig | Startup. The list of checked boxes you see is all programs and applications running in the background from boot on, and they are using your resources. You gain resources by unchecking the boxes which are safe to uncheck. Keep System Tray and Scan Registry. Keep entries related to H-P hardware. Other than that, it's up to you what is set to launch from your taskbar, and what you feel you can do without from there. If you have questions about any of the boxes, post a list of the questionable items, and someone here can help you decide what they are and what to do with them.
Prodigy's Tech-Support person has misled you; next time you call Prodigy, ask for a Senior HelpDesk Technician.
System resources, whether 63% or 0%, have absolutely nothing to do with your 26,400bps connect speed! Prodigy may be able to help you, but the actual problem is almost certainly the quality of your telephone line, so contact your local telephone company and ask what options you may have to improve your line quality. A dedicated digital line like most businesses use for their fax machines may be the best option. In many cases, Local Telephone providers will only guarantee a minimum modem connect speed of 2400bps, believe it or not.