Gotta run, so a quick reply...
Here's the deal. When you turn on your computer, the MB goes through a "pre-boot" sequence that is referred to as a "POST" - Power On Self Test. The POST starts when you see that first screen with the MSI logo... continues on through showing you the RAM size, HDDs connected, etc... and normally ends with a beep... where you'll then see the normal "starting Windows" screen. Everything in that POST process, from MSI logo to beep, is totally separate and has nothing to do with the OS - Windows. If you had a blank HDD, or no HDD, that post process should be the same. What this means, and your symptoms indicate, is that your problem is clearly hardware related... since your PC is not POST'ing consistently.
Not POSTing means a hardware problem and is most likely one of the core components... MB, CPU, PS, RAM, videocard. The quickest/easiest way, practically, to diagnose is trial and error by swapping each component with a known good component. You've already done this with the RAM, so that leaves 1 of the other 4 components as the problem. 2 of those components are very hard to swap - MB and CPU - so focus on the remaining 2 that are easy - video and PS. If you swap those two and still have problems, that leaves the MB/CPU... which basically means you're FUBAR'd anyway. New rig time.
As far as flashing the MB, sure you can try that, but I'd say it's a very low probability of fixing anything. You'll need to goto the MSI website, download the latest BIOS for your MB, download whatever tool (software program normally) that installs the BIOS (or creates the boot floppy/CD), then follow the directions to flash.... normally is just booting off of a floppy/CD/USB with that BIOS install tool and new BIOS. Personally, I don't think this is your problem, or going to help, since the PC ran fine for years with the current BIOS... nothing has changed... and if the BIOS somehow got corrupted, the root cause is probably a bad MB anyways (e.g. NVRAM died). You also need to be very careful when flashing... lose power during the flash and your MB is toast.
It sounds like you have on-board video. If that's the case, the MB most likely has an AGP slot that will disable the on-board video when a secondary videocard is installed. I think this is your next step. If u need to borrow an AGP videocard, just yell.... I have several. I also have a spare PS if you want to borrow one of those too to test.