I'm not on a Windows machine, so I don't know how much help I can be, but I can tell you that it doesn't matter whether your computer is using Wi-Fi or ethernet. All that matters is that iCloud has access to the internet. The iPhone does need to be connected to Wi-Fi for Photo Stream to sync though; it won't work on the cell network.
Before we do any troubleshooting, follow the steps in this article to reset your Photo Stream, and see if it resolves the issue. http://support.apple.com/kb/HT4890
It sounds like you've followed the correct setup process, but it doesn't hurt to check again. Restart your computer and do a soft reset on your iPhone by holding down the power and home buttons until the Apple logo appears on the screen. Once both have restarted, make sure that you only have one iCloud account set up on each device, and that they are both configured with the same account. Ensure that Photo Stream is turned on for each device as well. For the iPhone, check under both the "iCloud" and the "Photos" tab. Next, click the "Options" button in iCloud Control Panel to make sure you have photos syncing to the correct folder. If the pictures are still not syncing, try placing an image in the "Uploads" folder on your computer to see if it will sync to iCloud. Also, be aware that Photo Stream will only sync pictures taken after it has been set up, so images you already had on your phone will not sync.
Try to provide some more information, such as any troubleshooting steps you have taken so far. Is anything else syncing between your computer and phone, such as calendars or bookmarks? Did you follow an online tutorial to set this up, or did you figure it out as you went along?
I hope this helps. Let me know if any of these steps fix your issue.
Message was edited by: mp3 Andrew