If this post can help another newbie troubleshoot a "Why is my Debian Squeeze box not generating any sound from the onboard sound controller?", then cool beans.
Since installing Squeeze 6.0.7 on a bare metal workstation, I could get video (e.g., Flash) but no audio whatsoever from the motherboard speaker output. My cheapo speakers worked fine when connected to a Windows notebook. So, some info on my machine ...
# uname -r
The audio controller:
# lspci -v -s 00:1b.0
00:1b.0 Audio device: Intel Corporation 7 Series/C210 Series Chipset Family High Definition Audio Controller (rev 04)
Subsystem: Biostar Microtech Int'l Corp Device 821e
Flags: bus master, fast devsel, latency 0, IRQ 22
Memory at f7210000 (64-bit, non-prefetchable) [size=16K]
Capabilities:  Power Management version 2
Capabilities:  MSI: Enable- Count=1/1 Maskable- 64bit+
Capabilities:  Express Root Complex Integrated Endpoint, MSI 00
Capabilities:  Virtual Channel
Capabilities:  Root Complex Link
Kernel driver in use: HDA Intel
I checked that various ALSA bits were installed and tried numerous other exotic troubleshooting steps at alsa.opensrc.org. Nothing.
Finally in frustration I cranked up the volume on the speakers all the way and heard muted sounds from Youtube clips. Smacked my forehead, jumped into the Gnome Volume Control widget and maxed out the Master and Front volume levels, backed off the speaker volume, and sound output was normal.
Sometimes, you have to ensure there is gas in the tank.