Ethernet Network Card Installation:

Typically an Ethernet network interface is built-in to most modern motherboards. Some computer systems, especially server systems, are equipped with two network interfaces built-in to the motherboard. Additional interfaces can be installed in extra PCI expansion slots.

Try the command lspci -vv to see if the hardware is detected properly, and which kernel module (if any) is being assigned:

01:00.0 Ethernet controller: Broadcom Corporation NetXtreme BCM5764M Gigabit Ethernet PCIe (rev 10)
    Subsystem: Hewlett-Packard Company Device 1309
    Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx+
    Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=fast >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-
    Latency: 0, Cache Line Size: 64 bytes
    Interrupt: pin A routed to IRQ 52
    Region 0: Memory at f7000000 (64-bit, non-prefetchable) [size=64K]
    Capabilities: <access denied>
    Kernel driver in use: tg3
    Kernel modules: tg3


...
...

37:09.0 Ethernet controller: Broadcom Corporation NetXtreme BCM5782 Gigabit Ethernet (rev 03)
    Subsystem: Hewlett-Packard Company Device 000c
    Physical Slot: 5
    Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR+ FastB2B- DisINTx-
    Status: Cap+ 66MHz+ UDF- FastB2B+ ParErr- DEVSEL=medium >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-
    Latency: 32 (16000ns min), Cache Line Size: 64 bytes
    Interrupt: pin A routed to IRQ 21
    Region 0: Memory at f8000000 (64-bit, non-prefetchable) [size=64K]
    [virtual] Expansion ROM at f7100000 [disabled] [size=64K]
    Capabilities: <access denied>
    Kernel driver in use: tg3
    Kernel modules: tg3

or more specifically lspci -vv | grep Ethernet

01:00.0 Ethernet controller: Broadcom Corporation NetXtreme BCM5764M Gigabit Ethernet PCIe (rev 10)
37:09.0 Ethernet controller: Broadcom Corporation NetXtreme BCM5782 Gigabit Ethernet (rev 03)