Kernel.org: 5.1.4
sid (unstable): 4.19.37-3
buster (testing): 4.19.37-3
stretch (stable): 4.9.168-1+deb9u2
jessie (oldstable): 3.16.64-2

Debian GNU/Linux device driver check & report

Compaq: Presario v2310

PCI IDWorks?VendorDeviceDriverKernel
10024370YesATI Technologies IncIXP SB400 AC'97 Audio Controllersnd-atiixpv2.6.25-
10024371ATI Technologies IncIXP SB400 PCI-PCI Bridge
10024372YesATI Technologies IncIXP SB400 SMBus Controlleri2c-piix4v2.6.25-
10024373ATI Technologies IncIXP SB400 USB2 Host Controller
10024374ATI Technologies IncIXP SB400 USB Host Controller
10024375ATI Technologies IncIXP SB400 USB Host Controller
10024376YesATI Technologies IncIXP SB400 IDE Controllerpata_atiixpv2.6.25-
10024377ATI Technologies IncIXP SB400 PCI-ISA Bridge
10024378YesATI Technologies IncSB400 AC'97 Modem Controllersnd-atiixp-modemv2.6.25-
10025950ATI Technologies IncRS480 Host Bridge
10025955YesATI Technologies IncRadeon XPRESS 200M 5955 (PCIE)radeonfbv2.6.25-
10025a3fATI Technologies IncRS480 PCI Bridge
104c8031YesTexas InstrumentsPCIxx21/x515 Cardbus Controlleryenta_socketv2.6.25-
104c8032Texas InstrumentsOHCI Compliant IEEE 1394 Host Controller
104c8033YesTexas InstrumentsPCIxx21 Integrated FlashMedia Controllertifm_7xx1v2.6.25-
104c8034YesTexas InstrumentsPCI6411/6421/6611/6621/7411/7421/7611/7621 Secure Digital Controllersdhci
10ec8139YesRealtek Semiconductor Co., Ltd.RTL-8139/8139C/8139C+8139cp,8139toov2.6.25-
14e44318YesBroadcom CorporationBCM4318 [AirForce One 54g] 802.11g Wireless LAN Controllerssbv2.6.25-

USB Host controllers work
Broadcom wireless card works with ndiswrapper as documented at http://www.iit.edu/~kbloom1/Main/Compaq_Presario_v2310us
I don't know what the various other kinds of bridges are, but I assume they're kind of essential to the system so they must work.

Use kernel 2.6.11 or later.