I guess I was lucky with my N400c flash.
Maintenance was increasing on it, including replacing the LCD from one bought on ebay sor $50 so I bought a new notebook and made my N400c a play notebook.
I tried installing Linux on it but the touchpad refused to work. After hours of searching I discovered that the Compaq business notebooks had issues of the touchpad not working with Linux but that there was a New BIOS that fixed this.
I downloaded the Windows version of the BIOS you mention (HPQFlash for HP Notebook System BIOS (686AW) - Windows-based version 2004.03.08 8 Mar 04) and prepared by running virus scan and spy remover and minimized everything running and what was set to run on startup. I charged up the battery and put the notebook on my desk with everything around it cleaned up and away from the notebook and ran it on AC. I had made certain I was running stable for the last couple of days with no errors or freezing and had recently reformatted /Partitionedand put a fresh Windows XP Install and I took off the linux/grub and did everything I could think of to prevent a bad flash.
Well it paid off for me and the flash worked like a charm. Took about 6 minutes including restart.
As to your particular problem these notebooks are dirt cheap on ebay now with a price of $200-$300 and work great, especially for internet.
You can find dead or stripped ones for about $100 and thats what I would recommend unless you find value in conquering the beast and like hunting for the new chip and successfully swapping it out. You will spend far more than $100 of your time doing this though and may not succeed in the end on the $200 notebook.
I could not find any on ebay just now but typically there are several each week that are dead "parts" machines. Sometimes they even have lots of 4 that sell for like $400. I have been considering getting a N410c board/dead machine for the motherboard and CPU and upgrading with my N400c. I did find one of these on ebay UK which will probably sell at about $100 US and here is the link to that one.http://cgi.ebay.co.uk/ws/eBayISAPI.dll?ViewItem&category=3712&item=6752983884&rd=1
If you set up a search and check it three times a week you should end up finding 3 to 5 per week that will meet your needs for this project and sometimes you can get lucky finding one thats partially stripped (no HD, memory, AC, battery) for less than $50 since all you are after is the motherboard
I would have more fun mixing and matching parts from two machines than trying to replace the BIOS chip, plus the chances of success are greater and you can upgrade in the process to say an 850Mhz or an N410c 1.0Ghz or 1.2Ghz machine. You will then have plenty of spare parts for future problems or if you do not wish to keep them then after certifying them as good by testing them in your working notebook you can sell them on ebay as "tested and working part with DOA garauntee" and probably come out ahead, at least in $$, though at a big price in your time.
GOOD LUCK MY FRIEND!