Fresh Ubuntu 12.10 64-bit install on a Dell Vostro 3700 with intel integrated graphics and nvidia GT 330M.
An LG TV is connected to the laptop via a HDMI cable. The HDMI option appears in Settings -> Display and the additional desktop area is there if I hit Super + S, but there is no output on the TV and the TV does not appear as an option in Settings -> Sound.

I've tried different cables and HDMI ports, but the problem is most probably not there (since Ubuntu recognizes the TV and the TV works perfectly with another laptop with Ubuntu 12.10).
Reboot, logging in again didn't help either.

I installed the nvidia current driver (after installing build-essential, linux-source and the appropriate linux headers), but it failed to work together with Unity. :/

I've browsed all the HDMI topics on this forum and I've spent my day with google, yet haven't found any solution.

I would highly appreciate ANY help or hint, I really want the HDMI to work.
Please let me know if I should provide any further information.

System details in pastebin:

And here:
  1. dualon@alpha-neuron:~$ uname -a Linux alpha-neuron 3.5.0-21-generic #32-Ubuntu SMP Tue Dec 11 18:51:59 UTC 2012 x86_64 x86_64 x86_64 GNU/Linux dualon@alpha-neuron:~$ sudo lshw -c display *-display description: VGA compatible controller product: GT216 [GeForce GT 330M] vendor: NVIDIA Corporation physical id: 0 bus info: pci@0000:01:00.0 version: a2 width: 64 bits clock: 33MHz capabilities: pm msi pciexpress vga_controller bus_master cap_list rom configuration: driver=nouveau latency=0 resources: irq:16 memory:f9000000-f9ffffff memory:c0000000-cfffffff memory:d0000000-d1ffffff ioport:e000(size=128) memory:fa000000-fa07ffff *-display description: VGA compatible controller product: Core Processor Integrated Graphics Controller vendor: Intel Corporation physical id: 2 bus info: pci@0000:00:02.0 version: 18 width: 64 bits clock: 33MHz capabilities: msi pm vga_controller bus_master cap_list rom configuration: driver=i915 latency=0 resources: irq:48 memory:fa400000-fa7fffff memory:b0000000-bfffffff ioport:f080(size=8) dualon@alpha-neuron:~$ xrandr | grep HDMI HDMI1 connected 1920x1080+1600+0 (normal left inverted right x axis y axis) 160mm x 90mm dualon@alpha-neuron:~$ lsmod | grep hdmi snd_hda_codec_hdmi 32007 4 snd_hda_codec 134212 3 snd_hda_codec_hdmi,snd_hda_codec_idt,snd_hda_intel snd_pcm 96580 4 snd_hda_codec_hdmi,snd_usb_audio,snd_hda_intel,snd_hda_codec snd 78734 26 snd_hda_codec_hdmi,snd_usb_audio,snd_hda_codec_idt,snd_usbmidi_lib,snd_hda_intel,snd_hda_codec,snd_hwdep,snd_pcm,snd_rawmidi,snd_seq,snd_timer,snd_seq_device