Chipset drivers install without a blue screen for the first time
miss BSOD in previous answers, my bad, is it happens if you install chipset drivers and reboot after it before proceeding with further ones, or you bulk install everything? (i had similar issue with Creative sound cards, it was demo-registration program it loads first time after installing software package and reboot, if you remove it in registry before rebooting there are will be no BSOD)
Last try for drivers - boot with logging and examine bootlog.txt. Also load in command prompt mode and run Scandisk after unsuccessful boot and examine what it found, expect lost files and fragments, not just incorrect free space. Try to boot in safe mode after you can't normally.
If we assume mobo is dying there are several suspects: south bridge - temperature too high to sustain putting finger on it longer than few seconds (ICH5 is notorious for being damaged due to cheap and poor implementation of protection on inputs by mobo makers), overheating north bridge (but i think with such problem it will never pass memtest), CPU socket with broken and/or cold joints (could be checked by applying external pressure to mobo back during operation). Last one could be CPU VRM, but with hours of memtest and prime it must be dead and it's hardly possible that it will contribute to continuously growing cumulative errors leading to freeze and inability to boot.
On Hiren's boot cd you must have Victoria or MHDD, low level HDD surface test. Run it, if you encounter uncorrectable errors during read, run it again with zeroing surface and repeat read test.
Did you tried single channel mode for RAM?
Did you tried to install WinXP again and got same copy errors after changing RAM and especially single channel? You may have damaged CD or dying drive who knows, but it will be informative to do this.
Replace PSU. Or measure old, but if voltages within 10% margin it wouldn't help unless you inspect it with oscilloscope, because first victim of ripple noise is always hdd.
Maybe you have spare IDE drive, try with it. If it happen to work, then maybe you have incompatibility between your current SATA hdd firmware and first gen sata implementation in ICH5. Seagate Barracuda 7200.7/8 known to have issues with nForce and Silicon Image controllers, some WD drives have issues with first gen VIA or first gen in general.
Next stop googling every option in BIOS, disabling unneeded, trying to understand what happens with IRQ (during post and after loading Windows) and address mappings, changing ACPI modes (if you have such option).
Now you may understand how it's great to work in tech support and why swapping is sometimes lifesaver. 😀