I've been trying to get HDMI with sound working for the last few days, and I'm a little bit out of ideas. (I've verified that the hardware/Setup works via Windows.)

aplay does not list my HDMI device:

$ aplay -l
**** List of PLAYBACK Hardware Devices ****
card 0: NVidia [HDA NVidia], device 0: ALC662 rev1 Analog [ALC662 rev1 Analog]
  Subdevices: 1/1
  Subdevice #0: subdevice #0
card 0: NVidia [HDA NVidia], device 1: ALC662 rev1 Digital [ALC662 rev1 Digital]
  Subdevices: 1/1
  Subdevice #0: subdevice #0

I've already compiled the alsa drivers (1.0.24) from a snapshot (with --with-oss=no) and added the line

options snd-hda-intel model=auto    # Tried 3stack-dig and 6stack-dig too

to /etc/modprobe.d/alsa-base.conf. Still, the device does not show up.

If it is important, the HDMI TV is at the moment not configured to be part of the X session (I've tried that to, at least with X restart, and it didn't change anything).

What did I miss?

$ lspci
00:00.0 Host bridge: nVidia Corporation Device 07c3 (rev a2)
00:00.1 RAM memory: nVidia Corporation nForce 630i memory controller (rev a2)
00:01.0 RAM memory: nVidia Corporation nForce 630i memory controller (rev a1)
00:01.1 RAM memory: nVidia Corporation nForce 630i memory controller (rev a1)
00:01.2 RAM memory: nVidia Corporation nForce 630i memory controller (rev a1)
00:01.3 RAM memory: nVidia Corporation nForce 630i memory controller (rev a1)
00:01.4 RAM memory: nVidia Corporation nForce 630i memory controller (rev a1)
00:01.5 RAM memory: nVidia Corporation nForce 630i memory controller (rev a1)
00:01.6 RAM memory: nVidia Corporation nForce 630i memory controller (rev a1)
00:02.0 RAM memory: nVidia Corporation nForce 630i memory controller (rev a1)
00:03.0 ISA bridge: nVidia Corporation MCP73 LPC Bridge (rev a2)
00:03.1 SMBus: nVidia Corporation MCP73 SMBus (rev a1)
00:03.2 RAM memory: nVidia Corporation MCP73 Memory Controller (rev a1)
00:03.4 RAM memory: nVidia Corporation MCP73 Memory Controller (rev a1)
00:04.0 USB Controller: nVidia Corporation GeForce 7100/nForce 630i USB (rev a1)
00:04.1 USB Controller: nVidia Corporation MCP73 [nForce 630i] USB 2.0 Controller (EHCI) (rev a1)
00:08.0 IDE interface: nVidia Corporation MCP73 IDE (rev a1)
00:09.0 Audio device: nVidia Corporation MCP73 High Definition Audio (rev a1)
00:0a.0 PCI bridge: nVidia Corporation MCP73 PCI Express bridge (rev a1)
00:0b.0 PCI bridge: nVidia Corporation MCP73 PCI Express bridge (rev a1)
00:0c.0 PCI bridge: nVidia Corporation MCP73 PCI Express bridge (rev a1)
00:0d.0 PCI bridge: nVidia Corporation MCP73 PCI Express bridge (rev a1)
00:0e.0 IDE interface: nVidia Corporation MCP73 IDE (rev a2)
00:0f.0 Ethernet controller: nVidia Corporation MCP73 Ethernet (rev a2)
02:00.0 VGA compatible controller: nVidia Corporation G94 [GeForce 9600 GT] (rev a1)

$ aplay -L
default
pulse
    Playback/recording through the PulseAudio sound server
front:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    Front speakers
surround40:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    4.0 Surround output to Front and Rear speakers
surround41:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    4.1 Surround output to Front, Rear and Subwoofer speakers
surround50:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    5.0 Surround output to Front, Center and Rear speakers
surround51:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    5.1 Surround output to Front, Center, Rear and Subwoofer speakers
surround71:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    7.1 Surround output to Front, Center, Side, Rear and Woofer speakers
iec958:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Digital
    IEC958 (S/PDIF) Digital Audio Output
dmix:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    Direct sample mixing device
dmix:CARD=NVidia,DEV=1
    HDA NVidia, ALC662 rev1 Digital
    Direct sample mixing device
dsnoop:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    Direct sample snooping device
dsnoop:CARD=NVidia,DEV=1
    HDA NVidia, ALC662 rev1 Digital
    Direct sample snooping device
hw:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    Direct hardware device without any conversions
hw:CARD=NVidia,DEV=1
    HDA NVidia, ALC662 rev1 Digital
    Direct hardware device without any conversions
plughw:CARD=NVidia,DEV=0
    HDA NVidia, ALC662 rev1 Analog
    Hardware device with all software conversions
plughw:CARD=NVidia,DEV=1
    HDA NVidia, ALC662 rev1 Digital
    Hardware device with all software conversions