If the 3Ds turns off automatically directly at Boot, without showing any Screen before Shutting Down, its a sight that the CFW is installed Successfully (in my Eyes).
You just need to find a way to Boot your 3Ds, and it works only with a SD Card where you have still all Contents inside the SD Card. I cant Imagine that your 3Ds wont work even if you have really still all Contents on your SD Card. Maybe a SD Card Problem ?
You can try to find a SD Card or buy a cheap one with 2GB or something (Just for Testing) and Copying and Pasting again all of your Stuffs,Contents,Backups of the CFW Installation Progess on your new bought SD Card, and trying then Boot your 3Ds.
ps. I used earlier a normal 2GB SD Card (This was not the ORIGINAL SD Card of my O3DS XL, but i doed it anyway) and i remember the SD Card was very Old and a little bit "Dirty". I know that sometimes my 3Ds wont boot while the SD Card was inside my 3Ds. Then i reinserted it, and it still wont work, and i reinserted it AGAIN, and AGAIN, over 5 Times and then it Bootet. After i had to put my SD Card on the PC, same Problem started on my PC, so i had to reinsert all the time until my PC finds it.
And after i was done with Copying etc. i had to put Back the SD Card (XD) and again same Problem on my 3Ds -> Reinserting until it boots. I figure out it was a SD Card Problem (Your SD Card is maybe not Old, but a new SD Card for Testing, cant hurt^^).
I have no matter anymore, i hope you find a way.
