It could be the keyboard.
Though, I am unhappy to report that while I'd been happily recommending the Xmidi 1x1 for something like six years now, in the last two months there has been a huge increase in the number of reports I've heard from people having trouble with it. That is, from zero reports in six years to several all at once in the span of a couple weeks.
I contacted E-MU and they confirmed something strange seemed to be happening. That was already a couple months ago, and the reports have died back down to almost nothing again, but I'm worried that here-and-there some of the same bad batch of adapters are lingering on store/warehouse shelves.
The behavior you described is the same I've heard from others: the light turns on, but never flashes to indicate data is being sent. E-MU recommended trying to acquire a replacement through the store you ordered from, or failing that, through E-MU support. I tried to press them about the lengths they might be able to go to in order to avoid making this a very negative experience for customers, but they confirmed customers would have to cover shipping charges themselves to send it back to E-MU.
Each time I hear about this, I feel really bad about maintaining the recommendation on the site. I was hoping the problem would go away on its own, quickly. And while it has certainly all but disappeared, each time someone reports they're having a poor experience, I can't help but feel completely responsible. I am sorry.
Depending on where you got the adapter, I'd say return it to maybe try a different brand. Or, if you don't mind throwing the dice again and hoping not to get another dud, you could get a replacement Xmidi 1x1.