I posted this same issue on another forum (
http://www.virtualdr.com/) and luckily got the clue I needed to solve this problem. Thought I would share the knowledge here.
In the Netgear Wireless Settings, there is a place to enter a "Security Encryption (WEP) Key". It has a field where you can enter your "passphrase". After you enter your secret word and click the "Generate" button, the Netgear software creates FOUR different Keys (labeled "key 1," "key 2," "key 3," and "key 4," each one being a unique alphanumeric string or characters (length depends on whether your encryption strength is 64bit or 128bit). In your Wireless Connection Properties (on the computer that you intend you connect via the Netgear router), in the Wireless Networks tab, click the name of your network (should be visible in the "Preferred networks" section) and click the "Properties" button. In the "Network key" field (which by default shows 8 "bullet" characters to hide the real text), type the generated text from "key 1" in your Netgear Wireless Settings, NOT the passphrase used to generate the codes. And retype the code text in the "confirm network key" field, make sure the number in the "Key index (advanced)" field is "1", then click OK. You computer may try to log on automatically to your preferred network or you may need to select your network in Wireless Network Connection window and click "Connect."
What confused me was the Network Key field in Windows, and how it only has one field to enter a code. I always assumed that is where I type my "passphrase" and not the actual code (and the HP techs didn't realize that either). The Netgear software (and others, including the AirLink software that came with the USB wireless adapter I am using with another computer) has 4 fields for 4 different codes. So even non-computer-guru people like me can figure out that Netgear makes 4 codes, type those 4 codes in here. Note when I typed in the WEP code into my HP network properties, I typed the one from the "key 1" field that Netgear generated. I tried changing the "key index (advanced)" number to "2" and used the code from the Netgear "key 2" field, and that worked too. Not sure why it gives the option of keys 1, 2, 3 or 4, but it does. Just make sure that your number for "key index (advanced)" matches the Netgear key code you are typing into the WEP "Network key" fields in your wireless network properties window.