Kernel.org: 5.1.10
sid (unstable): 4.19.37-3
buster (testing): 4.19.37-3
stretch (stable): 4.9.168-1+deb9u2
jessie (oldstable): 3.16.68-1

Debian GNU/Linux device driver check & report

-assembled: T3310/DT230

PCI IDWorks?VendorDeviceDriverKernel
10390671YesSilicon Integrated Systems [SiS]671MXsis-agp
10390003YesSilicon Integrated Systems [SiS]AGP Port (virtual PCI-to-PCI bridge)sis
10390968Silicon Integrated Systems [SiS]SiS968 [MuTIOL Media IO]
10395513YesSilicon Integrated Systems [SiS]5513 IDE Controllerpata_sisv2.6.25-
10397001YesSilicon Integrated Systems [SiS]USB 1.1 Controllerusb-ohci,ohci-hcd
10397001YesSilicon Integrated Systems [SiS]USB 1.1 Controllerusb-ohci,ohci-hcd
10397002YesSilicon Integrated Systems [SiS]USB 2.0 Controllerusb-ehci,ehci-hcd
10391185YesSilicon Integrated Systems [SiS]AHCI IDE Controller (0106)ahciv2.6.25-
1039000aSilicon Integrated Systems [SiS]PCI-to-PCI bridge
1039000aSilicon Integrated Systems [SiS]PCI-to-PCI bridge
10390004Silicon Integrated Systems [SiS]PCI-to-PCI bridge
10396351Silicon Integrated Systems [SiS]771/671 PCIE VGA Display Adapter
10ec8136YesRealtek Semiconductor Co., Ltd.RTL8101E/RTL8102E PCI Express Fast Ethernet controllerr8169
10ec8168YesRealtek Semiconductor Co., Ltd.RTL8111/8168/8411 PCI Express Gigabit Ethernet Controllerr8169

イーサドライバはr8169ではなくr8168をコンパイルして導入する必要があります。
RTL8101E/RTL8102Eについてはまだうまく動作していません。