Restored Computer, Missing Drivers, Cannot Connect to Internet

My friends dad is very knowledgeable about computers, so I may be able to get some help from him, but he is busy most of the time.  I have tried switching its slots, I have verified that the lights are on, and its in its slot pretty well so I'm not sure what else it could be either.  I really appreciate your persistence and going to a repair shop wouldn't be such a bad thing.

I'm sorry that this has turned into such a saga.

About the only things I can think of now are:

1. The card wasn't re-seated properly in the slot.  Make sure it's pushed down all the way.  Or take it out and carefully put it back in, making sure everything is lined up properly.
2. The card is defective.
3. The PCI slot has a problem.  If the second PCI slot (the other white connector) is empty, you can try moving it there.

This wireless adapter should be in one of the two white connectors at the upper left of this figure:

The following is all that the Trendnet installation guide has to say on this issue:

Windows is unable to recognize my hardware. What should I do?

1. Make sure your computer meets the minimum requirements as specified in Section 1 of this

quick installation guide.  [Your computer does meet these requirements]

2. You must complete the installation of the wireless adapter configuration utility (as described in

Section 2) before connecting the Wireless Adapter to your computer.

3. Connect the Wireless Adapter to a different PCI slot on your computer.

Also note the following regarding the lights:

Check the installation

The LEDs of the Wireless LAN Adapter are clearly visible and the status of the

network link can be seen instantly:

1. Once the device is plugged to the station’s PCI slot, the LED of the Wireless

LAN Adapter will light up indicating a normal status.

2. When the device plugged to the station’s PCI slot and the driver was installed,

the ACT will start alternate blinking, it means that the device is starting to scan

the wireless devices near the Wireless LAN Adapter.

3. While the Wireless LAN Adapter linked up and transmitting data to the Access

Point or to other Wireless LAN station, the Link LED will lighted green.

If re-seating the card or moving it to the other PCI slot doesn't solve it, I'm afraid you'll have to take the computer to a local repair shop for some hands-on diagnosing. If you do, I suggest not going to a chain store but to an independent shop -- ask your friends with computers for recommendations. 

Alternately, you can buy a new wireless adapter.  You can get a USB adapter (which won't require you to open the case to install it) or you can buy a new internal adapter.  These days, you'll be more likely to find a PCIe card than a PCI card such as the one you have now.  Your motherboard has both PCI and PCIe connectors:  the PCI slots are white and the PCIe slots are green.

Ok so I have properly installed the drivers and put back in the adapter, but when I run their utility, it tells me that the adapter is not present, even though the lights are on, on it.  Also when I look at the Other devices category, Network Controller has been removed but there are no new drivers under Network Adapters.

You almost have it.

The TEW-623PI is a TRENDnet PCI wireless adapter.  The only problem is that there are two different versions, which require different drivers.  Look again and see if you can see whether you have Version 2.0R (info and driver download HERE) or Version 3.0R (info and driver download HERE). 

The installation for these files is quite a bit easier:  there's a Quick Installation Guide (scroll down the page and click the link).

Actually, the Quick Installation Guide wants you to install the driver BEFORE the device is physically installed in the computer.  So, turn the power off, touch the case with your hand to discharge any static electricity, and carefully remove the card.  There probably will be one screw holding the card in (if the screw is present, it will be in the slot at the top of the bracket -- see arrow):

Then gently but firmly pull the card up. It probably will be easier to remove if you unscrew the 3 antennas.  You may have to pull one end of the card up first; just don't rock the card side-to-side.

Once the card is out of the computer, you should be able to more easily see if you have version 2 or version 3.  And, while the card is out and you have more room, do yourself and your computer a favor:  buy a can of compressed air and blow out all the dust.

The download from Trendnet installs a configuration utility for the adapter.  To learn how to use this, download the User Guide, link at the bottom of the support page.

Ok so the thing that I'm pretty sure is the wireless adapter is triangular, but I can't read anything very well because it is very dusty and almost directly beneath another component.  The only thing I got off of it was tew623.  Sorry I can't be more specific about that.  When I tried to update the Network Controller driver it said that I didn't have the necessary files or something.