Well Brian you're at least in the right place. I suspect the problem is that the kl model is sort of an oddball, nearly all the tf700s are tf700t, and the two just won't mix. The good news is that a search of Asus' website for "TF700KL" does turn up something! Lately it's been hit-or-miss but you must've gone to church on Sunday. So you need to determine whether your KL is WW or VF (those are the only two options listed). When you boot with the volume-down key held, you should boot into a screen with 3 (or 4) icons, one flashing, and some tiny text up in the top left corner (if it's the same as most TFs) that says something like "released by epad_user_WW-22.214.171.124" or some such similar. You may need a magnifying glass to read it, I know I do these days. But it's the WW or VF part we need to know right now, so you know which firmware to download. This is a .zip file, now many of the TF firmware files are .zips within a .zip, so that you need to unzip it JUST ONCE and copy it to the SD card. Sometimes you have to rename it, also, but I'm not sure if that applies to the KL or no. Try it without first. Here is the page:
Go to the "Drivers and Firmware" page, select Android as OS, look for the latest firmware for either WW or VF, whichever your tablet is. (I haven't run into VF before, I have no idea what it means. WW stands for WorldWide, and usually means Europe and, IIRC, Africa and the Middle East). The rest is in this guide:
Let us know how you get on, OK?