No Recognition of ASIN or EAN Numbers after Installation

That is a valid but perhaps a misleading message. Check your error logs... you may likely see something like

Error retrieving Amazon item AWS.InvalidAccount, message: Your AccessKey Id is not registered for Product Advertising API. Please use the AccessKey Id obtained after registering at https://affiliate-program.amazon.com/gp/flex/advertising/api/sign-in.html.

This is an AMAZON problem, not a module problem.
23 emails and counting. Amazon still have not provided a resolution. They have a whacko setup with 3 - 4 different IDs and account requirements. In my case, this is their latest non-helpful email.

Upon researching your account I see that the Access Key: XXXXXXXXXXX that you are trying to use is linked to Amazon Web Services (which is what the error message says is required and which provides the ID needed to set up the module), not Product Advertising API (which provides neither of the IDs required to set up the module and is NOT referenced by anything -- other than Amazon non-tech support) and this is why you are receiving the error message stating that your Access Key ID is not registered for Product Advertising API.

Secondly, I noticed that you had questions regarding having to enter your Credit Card information to sign up for the Amazon Associates Program. I apologize for any frustrations you have experienced with this. Please understand the email you received that email from Amazon Web Services as they require that information, not Amazon Associates. Amazon Associates is free and we do not require that information.

When you are going through the steps to sign up for Product Advertising API you will just bypass entering this information. (Mind, this is in reply to the 20th email wherein a previous person -- all 23 from different people -- said that I already had 2 accounts and that was what was causing the problem. So how is telling me to sign up for another account going to fix it?)

Suggestions from others (not Amazon) would be most welcome.

I'm having the same problem. The documentation instructions are very clear concerning the setup leading to the test. "If it succeeds, you're all set!" No information concerning what to do when the test is failing.

I do not have two Amazon accounts. I've given them my CC number, which was a surprising requirement, considering we are supposed to be using free services. I've also received a confirmation email about the account creation. No EAN or ASIN numbers work in the test for me. Either Amazon has recently changed something that affects this module's setup, or I'm not smart enough to do what a couple thousand other people using this module have done, apparently successfully.

UPDATE:
I got it working. First, I want to mention something, although I have no idea if it matters. The documentation makes it seem as though signing up at both of these links is optional, that perhaps only the AWS link is required for signup.

http://aws.amazon.com/

I want to make it clear that I also signed up for the second link, the "you'll probably also want to..." link.

https://affiliate-program.amazon.com/gp/advertising/api/detail/main.html

I was always signed up for both and it wasn't originally working. I just want it to be clear I had signed up for both, in case it matters.

At any rate, after I got the confirmation email stating my AWS account had been successfully confirmed. About every five minutes, I saved the Amazon API settings again and then ran the test. I never changed anything about the settings. I just resaved. After a half hour of doing this, it suddenly started working. It may be that it just takes a while for the account to actually become functional after you receive the confirmation email.

That ASIN you used looks wrong. Try this one B004GXQOM0

Tried miketitsch's method -- turns out developers have to sign up advertising service as well to correctly retrieve product information from amazon product database. Thanks!