you probably need to buy a new one. im not sure about the size, though... you might want to try circuit city or radio shack.
For an Action Replay DSi, the connector is a 4-position Hirose Electric MQ-172 series. A connector end can be bought at Digi-Key (digikey.com), part number H10486-ND, for about $3.00. If you're up to a simple soldering job, you can wire it up to the end of a spare USB cable.
You can also get a complete replacement cable directly from Datel Gaming for around $10-$11 including shipping. If it doesn't bother you that your replacement cable is half the cost of the Action Replay, then the website is: http://www.datelgaming.com/ProductDetails.asp?ProductCode=DS%20AR%20-%20USB&Click=585
Or just go to http://www.datelcustomerservice.com
click on "Nintendo DS"
click on "Action Replay DSi"
click on "Q: How can I get a replacement cable for my Action Replay DSi?"
which will take you do the datelgaming.com site mentioned above.
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The Action Replay should have come with a CD to install the client software. This is how you access the codelists. With your Action Replay inserted into the DSi and connected to the PC by USB cable, you can copy the codes across to it using the client.
Most likely it's waiting or searching for an appropriate application to use for the action replay. If that application doesn't exist, your replay won't work either. Analogy: If there is no milk in the container in the fridge, trying to pour milk from it into a glass is rather futile as well.
On one side is a USB and the other has a mini USB
Your best bet is to buy an HDTV (if you haven't already) and then buy an HDMI cable, and also a component cable hookup for you in able to connect your Wii using the HDMI cable. Otherwise, USB cable won't do.
You can with a USB cable