My experience:
There is no TV/HDMI output until AFTER the Raspberry Pi has booted from the SD card.
If the red light is on, assume you have power. Watch the green light next to the red power LED when you power up the card, it shows read activity in the boot sequence.
If the green LED
- is faintly dim, there is no SD card.
- blinks once, then the firmware can't be loaded*
- 3 flashes: start.elf not found
- 4 flashes: start.elf not launched
- 7 flashes: kernel.img not found
*firmware not loading:
You need to create an image of the software onto the SD card. This is different than copying the the file to the SD card.
In my case I had the "Hynix" chip and I needed version 2013-02-09-wheezy-raspbian.zip (or later) from the downloads page. The soft-float release currently (3/20/2012 @ 7:54 PST) has an old date of 2012-02-08 which may not work with the Hynix chip.
I also found this wiki informative, but it did not mention my specific problem:
http://elinux.org/R-Pi_Troubleshooting