Kernel.org: , 
sid (unstable): 3.8.13-1
wheezy (testing): 3.2.41-2
kmuto bpo d-i: 
squeeze-bpo: 3.2.41-2+deb7u2~bpo60+1
squeeze (stable): 
lenny (oldstable): 

Debian GNU/Linux device driver check & report

HP: a1310n

PCI IDWorks?VendorDeviceDriverKernel
10025950ATI Technologies IncRS480 Host Bridge
10025a34ATI Technologies IncRS480 PCI-X Root Port
10024379YesATI Technologies IncIXP SB400 Serial ATA Controllersata_silv2.6.25-
10024374ATI Technologies IncIXP SB400 USB Host Controller
10024375ATI Technologies IncIXP SB400 USB Host Controller
10024373ATI Technologies IncIXP SB400 USB2 Host Controller
10024372YesATI Technologies IncIXP SB400 SMBus Controlleri2c-piix4v2.6.25-
10024376YesATI Technologies IncIXP SB400 IDE Controllerpata_atiixpv2.6.25-
10024377ATI Technologies IncIXP SB400 PCI-ISA Bridge
10024371ATI Technologies IncIXP SB400 PCI-PCI Bridge
10024370YesATI Technologies IncIXP SB400 AC'97 Audio Controllersnd-atiixpv2.6.25-
10221100Advanced Micro Devices [AMD]K8 [Athlon64/Opteron] HyperTransport Technology Configuration
10221101Advanced Micro Devices [AMD]K8 [Athlon64/Opteron] Address Map
10221102Advanced Micro Devices [AMD]K8 [Athlon64/Opteron] DRAM Controller
10221103YesAdvanced Micro Devices [AMD]K8 [Athlon64/Opteron] Miscellaneous Controlk8tempv2.6.25-
10025b60YesATI Technologies IncRV370 5B60 [Radeon X300 (PCIE)]radeonfbv2.6.25-
10025b70ATI Technologies IncRV370 [Radeon X300SE]
10ec8139YesRealtek Semiconductor Co., Ltd.RTL-8139/8139C/8139C+8139cp,8139toov2.6.25-
11063044YesVIA Technologies, Inc.VT6306/7/8 [Fire II(M)] IEEE 1394 OHCI Controllerohci1394
14f12f20Conexant Systems, Inc.HSF 56k Data/Fax Modem

It's working fine in Debian with a mix of testing/unstable.
The Basic X0rg 7.x is working but I haven't configured for dual heads or 3D.
My Ati X200 (onboard video) has completely disappeard from the mix (I think just due to the BIOS setting used to make the X300 primary)
All of your "Yes" results seem valid to me.