You forgot to do your homework on what cameras are included in the various versions of Adobe Camera Raw. The D7100 was included only weeks ago in the lastest version, which I think is 7.4. It is a new camera!
Elements 10 only goes through 6.7. It won't accept ACRs above that.
You still have a couple choices that don't require spending money. You can use the Nikon software to convert RAWs or the free downloadable Adobe DNG Converter.
On the otherhand, if you found the money for a D7100, you probably can affort to get some new software.
I bought a Sony RX100 and had the same issue. It was not included until 7.2. So, I used it as an excuse to upgrade to PSE 11 and Lightroom 4. While I was at it, I upgraded Premier Elements to 11.
When you get the new Elements 11 installed it probably won't work at first. It ships with an ACR earlier than 7.4. As soon as you get it installed, select Updates on the Help menu and it will fetch the lates ACR for you. Then your shiny new D7100 will be happy with Photoshop Elements.
I'm happy like a bear in the woods!
You either need PSE11 and ACR 7.4; or the free Adobe DNG Converter version 7.4 which will convert your D7100 RAW photos to DNG, and then PSE10 will work with them just fine; or use the Nikon software to convert the RAW files to TIF and use those in PSE.
I had the same problem. So I upgraded to Elements 11. As expected, the Nikon D7100 files were visible after i upgraded to Adobe Raw 7.4. This download is not available for Elements 10 apparently. However, not expected was that after installing the Adobe raw update, I could see my Nikon NEF files in Elements 10. those of you not wanting to go through the process of converting to jpeg or dng, I suggeest downloading the trial version of Elements 11. After updating Adobe Raw, check if you can see your Nikon D7100 files in Elements 10 Organizer. You may then not need to update! Post if this work around is successful.
Perhaps not. See my suggestion below.