I'm not even sure where to begin with this.  I have an EP35-DS3R that replaced an RMA's P35-DS3R, and I've had the same issues with both boards.  I've spent countless hours trying to fix this and I'm at a total loss.  I've been dealing with this for about three months.
 
Basically, I'm getting bluescreens followed by restarts a split-second later.  And I'm also getting all kinds of other random problems.  Numerous unrelated applications have crashed for no reason.  Just a few minutes ago, Windows XP suddenly showed my graphics card as unrecognized after being on for two hours.  I've had task manager refuse to run because it "required at least Windows 2000."  I've had files disappear from my HDD, including half the contents of system32 at one point.  This are just random examples of countless other bizarre problems.
 
After losing half of system32, I bought a new HDD and reinstalled XP there, with the same issues.  Switching around RAM hasn't helped, and I doubt I have four different bad sticks of Crucial Ballistix memory.  According to both Crucial and Gigabyte, the memory is supposed to be compatible with the board.  I've even check the PSU with a multimeter, and the voltages were fine on all rails.  And as I mentioned, I RMA'd the first MB (after it got stuck in a permanent reboot cycle) and still have the problems.  The second board now won't post unless I only use two out of four DIMMs.
 
I've tried two different graphics cards, and I've removed every single PCI card, and still had the problems.  I've used every BIOS setting and memory timing I can try to no avail.
 
I've even had both boards freeze on the BIOS screen a time or two.  But I've also been able to run Memtest for over eight hours without a single error  (and I've had it display multiple errors, but it may have been related to altered memory timings).  I've run CPU Burn-In for over an hour with no errors.  And I've used the computer for hours at a time with no issues.
 
The only thing I can think of at this point is to RMA the CPU itself (Q6600), but I'm just grasping straws at this point.  So I'm posting this in hopes that someone might have some suggestions.

what is your other system components? are all the other components are new?

You really need to post the rest of your components.
Personally I've had one of those boards die on me and it started acting very much like yours.
After enough times of trying to get in to the bios to see if something had changed along with numerous reboots with one memory stick or the other, drives plugged in or not  . . . the board wouldn't post.
I sent it back for a refund, I was really disappointed, it was running BOINC/Seti@home for two weeks strait without a problem with my Xeon3350 OC'd to 3.2Ghz.
 
The very first P35 board I got died after about two weeks too. (GA-P35-DS3L) That one either killed or was killed by a bad memory stick and a Samsung HDD.  
 
 

I had the same problems you have on my P35-DS4 and I was using ballistix 1066 memory.The first time my new build started the random reboots and bsod I rmad the memory and went to bestbuy and got a set of pny 667 memory which I still have thank goodness.Just today I did another rma of the ballistix. THE4th TIME. My rig runs fine on the pny. It does not like crucial ballistix.The first 3 sets died after about 10-14 days.The fourth after about 6-7 weeks.(I set the voltage manually.)Get another brand and save yourself a-lot of shipping money.And the other day I rebooted after the pc was on for 7-8 hours and my video card wasnt installed either.Its was like the drivers just uninstalled.And then the bsods started.

Gigabyte p35 boards don't like DDR2 dimms above DDR2 800. You can OC the DDR2 800 sticks, but the boards don't play nice with DDR2 1066, and so on.

The memory is Crucial Ballistix DDR800.  I overclocked it on the first board, but the second one I've only run at stock.  I've read a few instances of people having issues with Ballistix memory and these boards, but most of what I've seen was for DIMMs rated above DDR800.
 
For the other components:
As I mentioned, the processor is a Q6600.  My PSU is a 480W Enermax Noisetaker that's worked flawlessly in two previous systems.  My graphics card is an 8800GTS 512, and the second one I tried is a 7800GT.  I also have an Audigy 2 ZS in the system, although I've tried removing it to no effect.  Finally, the first HDD was a Western Digital 250GB SATA 3.0Gb/s, while the new one I bought is a 640GB WD.  The case is generic, but it has good airflow (the CPU stays below 50C, even at load).

I happen to stumble across some information, and apparently the Crucial DIMMs I have are from a batch they shipped out that had approximately an 80% failure rate.  So it looks like it really is possible that Crucial sent me 4/4 bad modules.  I'm going to just try a completely different brand of memory at this point and see how that does.
 
I've heard for years about how great Crucial is, and with dropping memory prices I figured I would try them.  It will probably be the last time I ever buy from them, as an 80% failure rate is inexcusable, IMO.  I'll probably think twice about buying Gigabyte as well, since these boards haven't exactly helped the situation (assuming bad memory is the main issue).  The first board wouldn't even post at all with some older Corsair DDR2-667 I had (the new one does though, and seems to be working fine with it in).
 
So hopefully this will get everything working.  If the board goes on and works wonderfully from now on with new memory, I might even be willing to overlook Gigabyte's part in all of this.