Your USB audio card is not recognized by the system, so squeezeslave will not see it either.
my aplay -L
dcerouter_1011439:/home/rperre# aplay -L
front:CARD=Live,DEV=0
SB Live! Value [CT4832], ADC Capture/Standard PCM Playback
Front speakers
rear:CARD=Live,DEV=0
SB Live! Value [CT4832], ADC Capture/Standard PCM Playback
Rear speakers
center_lfe:CARD=Live,DEV=0
SB Live! Value [CT4832], ADC Capture/Standard PCM Playback
Center and Subwoofer speakers
surround40:CARD=Live,DEV=0
SB Live! Value [CT4832], ADC Capture/Standard PCM Playback
4.0 Surround output to Front and Rear speakers
surround41:CARD=Live,DEV=0
SB Live! Value [CT4832], ADC Capture/Standard PCM Playback
4.1 Surround output to Front, Rear and Subwoofer speakers
surround50:CARD=Live,DEV=0
SB Live! Value [CT4832], ADC Capture/Standard PCM Playback
5.0 Surround output to Front, Center and Rear speakers
surround51:CARD=Live,DEV=0
SB Live! Value [CT4832], ADC Capture/Standard PCM Playback
5.1 Surround output to Front, Center, Rear and Subwoofer speakers
iec958:CARD=Live,DEV=0
SB Live! Value [CT4832], Multichannel Capture/PT Playback
IEC958 (S/PDIF) Digital Audio Output
null
Discard all samples (playback) or generate zero samples (capture)
front:CARD=Device,DEV=0
USB Audio Device, USB Audio
Front speakers
surround40:CARD=Device,DEV=0
USB Audio Device, USB Audio
4.0 Surround output to Front and Rear speakers
surround41:CARD=Device,DEV=0
USB Audio Device, USB Audio
4.1 Surround output to Front, Rear and Subwoofer speakers
surround50:CARD=Device,DEV=0
USB Audio Device, USB Audio
5.0 Surround output to Front, Center and Rear speakers
surround51:CARD=Device,DEV=0
USB Audio Device, USB Audio
5.1 Surround output to Front, Center, Rear and Subwoofer speakers
surround71:CARD=Device,DEV=0
USB Audio Device, USB Audio
7.1 Surround output to Front, Center, Side, Rear and Woofer speakers
iec958:CARD=Device,DEV=0
USB Audio Device, USB Audio
IEC958 (S/PDIF) Digital Audio Output
You can see that my USB Audio Device is showing in aplay and i also have a pci card in my core. Not sure why yours doesn't because it shows in lsusb. you have to look in dmesg or something to make sure the drivers get loaded.
You do have the latest version of squeezeslave, so that should not be the problem.
Richard