I just got RE1 working on WinXP SP2, Athlon XP 2800+, Geforce 6600GT following the instructions here.
The minute I saw that I had to set the compatibility mode to "Windows 95". I started checking for an application compatibility fix from Microsoft and sure enough there is one in their database. It didn't work for me because it relies on a file called retheme.zip to verify the correct program and it can't find it. I edited the entries and removed this file dependancy. I named the new compatibility database RE1full.sdb. I also created RE1minimal.sdb that will only fix ResidentEvil.exe and leaves out checker.exe, launch.exe, and setup.exe.
I suggest using this fix before installing the game. Download the attached file RE1.zip, extract, and install from command prompt or run box with the command: sdbinst re1full.sdb (or) sdbinst re1minimal.sdb .
I ripped my Resident Evil CD to hard drive with Nero Burning Rom using the filename RE1.NRG and mounted it into Daemon tools.
From there on out the program installed fine except for having to hit the ESCAPE key when the blank red screen came up. I installed nothing to the hard drive since the entire game is already running from a virtual CD-ROM image. I selected Rendition as the video driver.
The game runs way too fast and the only slowdown program I found to work well was Mo'Slo 4Biz's Slo'Win EZ component with speed set for 12.98 method 3 and interval 1. Using Mo'Slo the game does not crash during the initial Jill/Barry sequence when they run into the very first zombie in the dining room. You can collect the clips from Kenneth's body.
I found a command line file on the net that will setup all of the video modes for the game including the software modes. It is called setup.exe and is included in RE1.zip.
I had fun fooling around with this but realistically running the PSX version in either psxemu or ePSXe is a much better option.
EDIT: Major edits to the entire text of message and final change to RE1.zip attachment.