I downloaded the hard float image of Raspbian here:
http://www.raspberrypi.org/downloads
I copied the recommended hard-float image on an SD card and the Raspberry Pi boots fine with it.
Then I downloaded the soft-float version of Raspbian because I need it to get some software running that does not work on the hard-float version. I formatted the SD card again, copied the soft-float image onto it and tried to boot the Raspberry Pi with it.
Problem: the Raspbery Pi doesn't boot with the soft-float version of Raspbian!! I see the green "ACT" LED light up for less than a second. After that only the red power LED is on and nothing happens after that.
I repeated this process a couple of times and redownloaded the images, checked the SHA of the downloaded file, etc. It just doesn't work. The hard-float image always boots up (green "ACT" light flashes rapidly like normal).
Any ideas?
Update: If you have a newer Raspberry Pi with Hynix memory then the older versions of Raspbian will not boot. Specifically you'll need at least the 2013-02-09 Debian 7 (Wheezy) build. See this post.
Now, the 2013-02-09 Wheezy build is a hard-float version, so you can't use that, but you can update the kernel image of your soft-float version which is actually independent of the Linux OS (I'm told that basically the GPU boots the Raspberry Pi, and it runs the ARM as a kind of co-processor). So, you can run rpi-update to update your kernel, and it should be all OK.
There's a bit of a catch-22 if you don't own any of the older Raspberry Pis that will boot the older images--how can you update the OS if the only Raspberry Pi you have is a newer one which won't boot? In your case it sounds like you have access to an older one, so you're OK. For those who don't, maybe someone will eventually post an updated soft-float version, but until then perhaps you can try the following. I haven't; it's just a theory, but at this point you don't have much to lose :-)
Previous post: Yes, I had this same problem. I don't know exactly what is wrong, but the start_elf image won't boot, at least with the recent set of Raspberry Pis. I can't believe Raspbian would release something that broken, so I suspect it works for some Raspberry Pis, but not others. What you need to do is:
See my related post.