Modem will not work on restart

A few years ago my network connector (the one built into the motherboard) quit working. I had a network card, the type you install into an expansion slot in the back of the computer, which I installed. I can't remember if I had a driver on a disk or if it was just recognized by the computer, but it worked when I did a restart. Since then, every time I restart I get a message that there is no internet connection and I have to physically change the Ethernet cable on the back of my computer between the two ports. I've tried just unplugging and re-plugging the cable from the back of the modem, or from whichever port I have it plugged into on the back of my computer, but that does not work. I have to actually change to the other port. I've done half a dozen clean installs of the operating system (Vista with a 7 upgrade) without change.
Since I rarely shut down my computer, it's only a problem once a week when I go through the automatic update/restart scheduled. I've put up with this for 2-3 years and it works every time, but I've relocated my CPU and now instead of just tilting it forward and switching ports I have to crawl under my desk with a flashlight. I'm getting too old for that. Surely there's a simple fix?
Thanks

Thanks for your help sandravlado.

This is what I did: I shut down the computer. The Ethernet cable was plugged into the original port, ie: the one built into the motherboard. I left it there, took off the side of the CPU and removed the network card I had installed years ago when I first had the problem. I restarted and my home page came up fine. Then I did a restart and got this error message:





This page can’t be displayed

• Make sure the web address https://my.yahoo.com is correct.
• Look for the page with your search engine.
• Refresh the page in a few minutes.

When I clicked on "Details" I got this:
Details about network adapter diagnosis:

Network adapter Local Area Connection driver information:

Description . . . . . . . . . . : NVIDIA nForce Networking Controller
Manufacturer . . . . . . . . . : NVIDIA
Provider . . . . . . . . . . . : Microsoft
Version . . . . . . . . . . . : 1.0.1.211
Inf File Name . . . . . . . . . : C:\Windows\INF\netnvm32.inf
Inf File Date . . . . . . . . . : Monday, July 13, 2009 8:46:33 PM
Section Name . . . . . . . . . : NVENET51.NDI
Hardware ID . . . . . . . . . . : pci\ven_10de&dev_0269
Instance Status Flags . . . . . : 0x180200a
Device Manager Status Code . . : 0
IfType . . . . . . . . . . . . : 6
Physical Media Type . . . . . . : 14

All that means nothing to me, but it may to you, so sorry in advance if it's extraneous information, but I figured better more than less...

I restarted 5-6 times and did a complete shut down 3-4 times and could never get back to my home page... I kept getting the same error message, while plugging and unplugging the cable at various intervals during the restarts. I had to reinstall the network card (after cleaning connectors) in able to get back online, and it started doing exactly what it was doing before. Every restart I have to switch ports. What do you think?
Thanks

I think some screen prints will hlep.
Here is a tutorial by Brink for how to upload screen prints:
Screenshots and Files - Upload and Post in Seven Forums

Post a screen print of all your Network Adapters in Device Manager
To see these go to
Control Panel > Administrative Tools > Computer Management > Device Manager
Click on Network Adapters, to show all the devices
see my screen print 1 below for an example

Post a screen print of what you see in Network and Sharing Center
To see this go to Control Panel > Network and Sharing Center
see my screen print 2 below for an example

I would look at these if i had the issue you do ...

First I'd like to thank everyone who tried to help on this. The strangest thing happened....
As I said I'd lived with this problem for years, doing numerous clean installs with no change, but I was determined to try my best to fix it this time. I had went through all the procedures you had outlined as well as others with no results. A few hours later I was in the process of doing screenshots of the things you needed to help when, after a rest I came back and my monitor had turned itself off. When I moved my mouse an error screen came up with two options, said to choose using my arrow keys... and my keyboard would not work. Changed USB port, keyboards, did hard shutdown, nothing worked... no keyboard and screen frozen with error message. I powered down, unplugged & re-plugged my C Drive... no change. Got mad and unplugged C Drive while powered up, things really went south. To make a long story short, after hours of trying to use my Win7 repair disk and numerous other things and just getting messages to "contact equipment manufacturer" I did a clean install with Vista, did my 7 upgrade, and my computer works better than it has in years, including the Ethernet port on the motherboard working perfectly without having to change it every time I power up! So all is working well, and I credit all to a combination of all the fixes you had me try and my desperation and total lack of judgment in unplugging my hard drive while it was powered up. THANKS AGAIN to DavidE and sandravlado.