Hello all my name is Alex, and I'm very new to Linux! I have no idea how to get my sound to work on my machine. I'm running I guess the latest gnome PClinuxOS version on my HP dv2125nr Laptop. My friend told me it would be a easy transition from Win to linux so I thought I'd try it out. If anyone knows of a better distro Please let me know. I'm happy with the PCLinuxOS but if I could get the sound and wireless to work on another distro easier, I'll make the change. It took a bit for me to get my wireless to work but I had help from my friend. Unfortunately he will unable to help me for he has moved out of state. If you could help I would need step by step instuctions for i am dumb when it comes to Linux!

open a shell window and perform the following command:
This will list all pci devices that the OS can see. If your sound card is working Hardware wise, you will see a line which tells you the manufacturer of the card. If the command lists the card that means the OS CAN see the card but it doesn't have the driver to run it.

Please execute the command and post results and we will help you find a resource to install the card.

00:00.0 RAM memory: nVidia Corporation C51 Host Bridge (rev a2)
00:00.1 RAM memory: nVidia Corporation C51 Memory Controller 0 (rev a2)
00:00.2 RAM memory: nVidia Corporation C51 Memory Controller 1 (rev a2)
00:00.3 RAM memory: nVidia Corporation C51 Memory Controller 5 (rev a2)
00:00.4 RAM memory: nVidia Corporation C51 Memory Controller 4 (rev a2)
00:00.5 RAM memory: nVidia Corporation C51 Host Bridge (rev a2)
00:00.6 RAM memory: nVidia Corporation C51 Memory Controller 3 (rev a2)
00:00.7 RAM memory: nVidia Corporation C51 Memory Controller 2 (rev a2)
00:02.0 PCI bridge: nVidia Corporation C51 PCI Express Bridge (rev a1)
00:03.0 PCI bridge: nVidia Corporation C51 PCI Express Bridge (rev a1)
00:05.0 VGA compatible controller: nVidia Corporation C51 [Geforce 6150 Go] (rev a2)
00:09.0 RAM memory: nVidia Corporation MCP51 Host Bridge (rev a2)
00:0a.0 ISA bridge: nVidia Corporation MCP51 LPC Bridge (rev a3)
00:0a.1 SMBus: nVidia Corporation MCP51 SMBus (rev a3)
00:0a.3 Co-processor: nVidia Corporation MCP51 PMU (rev a3)
00:0b.0 USB Controller: nVidia Corporation MCP51 USB Controller (rev a3)
00:0b.1 USB Controller: nVidia Corporation MCP51 USB Controller (rev a3)
00:0d.0 IDE interface: nVidia Corporation MCP51 IDE (rev f1)
00:0e.0 IDE interface: nVidia Corporation MCP51 Serial ATA Controller (rev f1)
00:10.0 PCI bridge: nVidia Corporation MCP51 PCI Bridge (rev a2)
00:10.1 Audio device: nVidia Corporation MCP51 High Definition Audio (rev a2)
00:14.0 Bridge: nVidia Corporation MCP51 Ethernet Controller (rev a3)
00:18.0 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] HyperTransport Technology Configuration
00:18.1 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] Address Map
00:18.2 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] DRAM Controller
00:18.3 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] Miscellaneous Control
01:00.0 Network controller: Broadcom Corporation Dell Wireless 1390 WLAN Mini-PCI Card (rev 01)
03:09.0 FireWire (IEEE 1394): Ricoh Co Ltd R5C832 IEEE 1394 Controller
03:09.1 Generic system peripheral [0805]: Ricoh Co Ltd R5C822 SD/SDIO/MMC/MS/MSPro Host Adapter (rev 19)
03:09.2 System peripheral: Ricoh Co Ltd Unknown device 0843 (rev 01)
03:09.3 System peripheral: Ricoh Co Ltd R5C592 Memory Stick Bus Host Adapter (rev 0a)
03:09.4 System peripheral: Ricoh Co Ltd xD-Picture Card Controller (rev 05)

From the output you posted:
Apparently that's your Audio Card. I breifily googled the subject and i came across this page:http://jblevins.org/computing/linux/mcp51-alsa It explains installing the linux driver for the card.
note howlspsci -vv option which gives you more details about your PCI device.