CPUID: 0x10676, paired with ICH9 PCH, if I am not mistaken. Also, you are probably (almost for sure) using SeaBIOS as payload.
The thing which really confuses me is Debian Kernel command line: I am used 99% to RHEL/Fedora logs, so this command like is really confusing, since I could not determine too much about your GRUB2.
Here it is (too simplictic for me, should have much more in it): Command line: BOOT_IMAGE=(ahci0,msdos1)/vmlinuz root=/dev/sda1
And, after carefully examining PCIe bus, I found the ETH controller: 00:19.0 [VID=0x8086, DID=0x294C]:
https://pci-ids.ucw.cz/read/PC/8086/294c[user@localhost projects]$ cat dmesg.txt | grep 00:19.0
[ 0.151652] pci 0000:00:19.0:
[8086:294c] type 00 class 0x020000
[ 0.151694] pci 0000:00:19.0: reg 0x10: [mem 0xe1600000-0xe161ffff]
[ 0.151707] pci 0000:00:19.0: reg 0x14: [mem 0xe1624000-0xe1624fff]
[ 0.151721] pci 0000:00:19.0: reg 0x18: [io 0x3000-0x301f]
[ 0.151802] pci 0000:00:19.0: PME# supported from D0 D3hot D3cold
[ 1.489719] e1000e 0000:00:19.0: Interrupt Throttling Rate (ints/sec) set to dynamic conservative mode
[ 1.611526] e1000e 0000:00:19.0: The NVM Checksum Is Not Valid
[ 1.635873] e1000e: probe of 0000:00:19.0 failed with error -5[user@localhost projects]$
Now, I need from you the following: ifconfig -a (to see if your wired ETH controller is present there).