Delete the Verizon PPPOE connectoid in the network connections list. You won't need it anymore.
Use the network wizard to set up a new internet connection that is straight broadband/ethernet through a local area network. You don't have a LAN - yet - but don't let that get in the way of the wizard. You'll want it set to acquire an IP address automatically. Turn the computer off.
Take the ethenet wire between the modem and the computer and reconnect it to between LAN jack #1 on the router and the computer. In other words, you don't need to crawl under the desk to change the ethernet cable in the back of the computer. Take the new ethernet cord and connect it from to the modem (where you just took the other cable out) and the WAN jack on the back of the router.
Turn the router on.
Turn the computer on.
The computer should acquire an internal IP address from the router. Follow the router instructions (or run its wizard) for configuring a DSL connection, i.e., this is where you put the Verizon userID and password into the router.
At this point, you should be able to access the internet. Now you just need to tweak. Get DrTCP (google it, first item, download from Broadband Reports.com) and reset your computer MTU to 1492. This will be necessary if you hope email to go through (its just the way Verizon does it, so you have to do it their way...) Be sure to reset the MTU on any other computers using this connection if they will be sending Verizon email. Otherwise, resetting MTU is merely an efficiency tweak. The connection can live with the default 1500, but 1492 works better.
Get comfortable with the configuration interface of the D-Link - you will be using it a lot as you bring up the wireless security.
Attend to whatever is required for installing the WiFi card in the laptop. After you have installed it according to the manufacturer's instructions, go to the manufacturer's website to see if there are any firmware or driver updates. This is critical - with the rate that manufacturers are releasing firmware and driver patches these days, even brand new merchandise is obsolete until patched.
Establish an initial unsecured default WiFi connection between the laptop and the router access point. Windows will complain that you are being foolish to connect to an insecure location, but go with it for now. Gotta first make sure all drivers and hardware work in plain vanilla default mode. Review anything that doesn't work and get it working now.
When the connection works, start upgrading the security levels on the connection. Change the name of the SSID. Enable MAC filtering. Enable encryption. Deny wireless access to the router setup. Etc. But do it one step at a time. You'll have to bounce back and forth between the router setup screens which you'll be viewing from the wired connection and the configuration dialogs on the laptop. As each piece falls into place, go on to the next. This way you'll only have to fight with one setting or mis-typed passphrase at a time. Believe me, this can be nutty. You can't see what you typed behind the asterisks, so you have to be very careful to get it right at both ends.
When the wireless connection is working to your satisfaction from within the same room, take the laptop where ever it will reside and try again from there. If you start having connection problems, it is not a configuration issue (you already got that set up while in the same room), but rather is a signal range issue. Now you just have to play with the antenna positioning to get the signal strength right. Or do something more radical for improved signal penetration - but that's another topic which we shouldn't get into here, just be aware that it sometimes is an issue to deal with.