Having the same issue here. I'm using SanDisk Extreme HD Video 30MB/s SDHC I card (BI1205616252D)
I tried booting debian6-19-04-2012.img
Initially faced the problem of Red LED on + faint Green LED. After using rpi-updater in offline mode from my laptop, the Green LED remained always on. So far nothing. It is same as all of you are experiencing
Tried freezing, no effect.
However if I touch the solder pad of the connectors of the SD card slot, with my fingers (I'm just touching the soldered pads, NOT putting any mechanical force on the connector itself), the green LED starts flashing and I start seeing output on my monitor hooked up with a HDMI to DVI connector. It seems like the Pi is starting to read from the card and then gives up due to I/O errors. Here's a photograph that I had managed to take --

This indicates some electrical glitches on the data lines of the SD card. Touching the data lines, occasionally makes the thing work.
I do have access to high bandwidth scopes, but right now it is late night (almost early morning

) . Tomorrow, I can try probing the SD card data and clock lines and see if there's anything suspicious.
Meanwhile, it would be great, if someone can point out, if the Pi is using SPI or SD Bus ?