Download everything related to wireless from Dell first and keep track of where these files are being stored. Ensure that they are the correct drivers, for the correct model, etc.
Remove the existing drivers and its software bundle by uninstalling the Dell WiFi software in "Programs" if it is there.
Uninstall the card from "Device Manager". Make sure it is the right card.
Note: At this point you will have no Internet.
Restart the computer.
Begin the process of installing the Dell drivers and software. This will require an understanding of how the installation process works. Read the documentation. If possible, contact Dell for further instruction.
You will now need to create the link to your wireless connection once again.
Follow my advice about disabling IPv6 above. Consider disabling your LAN card under Network Connections by right-clicking on it and Disable. This is simply a good practice in general.
Set your WiFi card properties so that (as in the above article) it does not turn off. "Allow computer to turn off this device to save power" Uncheck.
These instructions are fairly vague. I would actually need to do a video or post a large amount of screenshots for the level of support you are requesting. In general, this is the procedure. What is important is that you perform the procedure properly and carefully. If you have any doubt about what you are doing, take a step back. I cannot provide phone support to you through the forums or remote support right now, or I would try to help. However, Dell Support may indeed assist you with this to get everything functioning properly.
I believe that by updating your wireless adapter and starting from a fairly clean slate, there is a good chance you will mitigate the problems you've been experiencing. Disabling IPv6 on a wireless card is a practice that is known to work for many routers whereas the connection becomes faulty. It is not the first time it has been done to correct the issue and likely not the last. However, there is no guarantee any of these steps will work. Making sure the computer is not turning off the card to save power is also an important step.
One other thing: Try using the card without the Dell WiFi software if you have it already. If the connection works without failure, you may not need it. Sometimes third-party software, even from Dell, can create problems with wireless connections. If you still experience problems, continue to install the software applications that are associated with this device which I do believe are and should be supplied by Dell.
Again, this is not a procedure that is easy for someone who is unfamiliar with changing around system settings, removing and adding devices, and especially performing networking tasks. Writing all of this on a forum post and hoping that you can get it done perfectly is not exactly the ideal method of assistance in your case. You really should be utilizing telephone or remote desktop support from the manufacturer in this case.
However, if you believe it is worth the risk of getting everything working properly, try making these changes. Since you can't use wireless properly right now anyway, for so long as you stick to the directions, the risk may be worth the reward of being able to use your wireless connection properly.
There is still a very good chance this is all due to some misconfiguration of your router, and if that is the case, you will need to consult with D-LINK. I have found that working with Cisco/Linksys over the phone on complex issues involving customer support in the past was never a problem. I have probably called D-link support as well, and they were good. They will usually support all devices and give you good instruction if you reach the appropriate support personnel and explain the problem to them in detail. This is the best information I can give you on properly reconfiguring the router portion if that is the issue. One way or another, there is an opportunity that these steps may solve your problem.
Relying on forums is an excellent choice in many instances, but if you get into a predicament where you seriously are not sure of what you are doing, and do not feel comfortable performing certain tasks to try and fix your system, you should always consider contacting manufacturers and working that angle as well.
I do apologize if my instructions have not been clear enough, but I am hopeful you are familiar with the concepts I have explained in the various posts in this thread. Good luck with this and here is hoping the WiFi will work again. If all else fails, there are always USB-based portable WiFi adapters you can buy as a last resort. However, that does indeed defeat the purpose of having a built-in card. I have replaced cards on laptops and know what I am talking about in this regard, but there is no guarantee and a large margin for error on this one.
Good luck and please let me know how it goes.