automatically connect to Ethernet at boot

We are using Windows 7x64 Ultimate in our office floor. Most are Dell, HP and Acer and others. All use Ethernet network cards connected to always on Cisco Linksys Broadband routers, ie, WRT54G and other models.
Often, after we boot, the computers will directly connected to the Internet.
However, many times, the computers do NOT connect to the internet. We have to bring up the Network and Sharing Center, then, click the red "X" mark to run the Windows Network Diagnostics. The dialog box will indicate "Windows tested your Internet connections and verified that you are able to access some websites. Are you looking for help with a different issue?" Then, the red "X" mark disappeared, and this computer is connected to the Internet.
What can we do to make the connection to Internet automatic every time we boot up?

Short answer is change the router. That is a very old model. I cannot comment on the other models you mention.I had the same problem until a few months ago. I spent several months and many 'phone calls trying to solve the problem. "experts" offered a lot of advice, none of which worked. You were lucky with your fix. The only thing which worked for me was a hard reset (with the small button on the back) and a log off/on.
I even accused my ISP of taking my line when it was inactive. I really believed that worked for a while, but I now think I was mistaken.
Reading up intensively, brought me to the conclusion that this was a common problem with Linksys, and partricularly that model. I now run a D-link and the problem, so far, has not re-occured

Playing on Dave's possible cause, it might be worth a try to update the routers firmware.

Yes. I did not mention that. I found (some months ago), that there was an update. Quite painless to install. Once again, peculiarly, it seemd to improve things, but only temporarily (Like a couple of weeks!)

Has anyone use this LSP-fix?
http://www.cexx.org/lspfix.htm

Is this LSP is the problem? Is Apple's "bonjour" messed up my network connection?

If you are using the Apple's "bonjour" then you need to change the Bonjour service from “automatic” to “automatic (delayed start)” on each W7 machine. And yes, it's possible, this could be causing your lack of internet on boot-up.

How do you set Apple Bonjour service? In control panel somewhere?

Reload with latest Cisco WRT54G firmware, version 1.02.8, 10/5/2009. Same problem. No difference.

http://www.sevenforums.com/tutorials...t-disable.html

OK, I checked, the "Bonjour Service" is "Disabled" at Startup Type.

This program is "c:\program files (x86)\Bonjour\mDNSResponder.exe"

I should set this "Bonjour Service" to "disable" correct?

If you use iTumes then you will want it running. You are not disabling things through MSCONFIG are you? because that is not correct. As in the article I pasted, you need to go to control panel \ Administrative Tools ... services; then find Bonjour and double-click on it to open properties and there set Start-up type to "Automatic (Delayed Start)" .... NOT DISABLED.

Now, are you saying it was ALREADY disabled? If so then you probably aren't using it and it isn't likely the cause of your problem and therefore not a solution either. However, If YOU set it to disabled please go back and set it to "Automatic (Delayed Start)" and if you changed anything in MSCONFIG then set that back to the way it was.

And this is a program, not a service. If it is in msconfig start-up then iTunes probably needs it so leave it.