BIOS Upgrade Necessary?

Specs:
Operating System- Microsoft Windows XP (SP3)
PC- Gateway Media Center Edition GT5014 2005
CPU- DualCore Intel Pentium D 820, 2800 MHz (14 x 200)
Motherboard- Intel Cortez D945GCZ (2 PCI, 1 PCI-E x1, 1 PCI-E x16, 4 DDR2 DIMM, Audio, Video, LAN)
Motherboard Chipset- Intel Lakeport-G i945G
System Memory- 1013 MB (DDR2-533 DDR2 SDRAM)
BIOS Type-Intel (09/15/05)
RAM Module- (2) Samsung M3 78T6553CZ3-CD5 512 MB

Alright, so SATA is running on one port (0) using 250 GB. We have no RAID in our system. Do I need to upgrade our BIOS? We're having error issues with memory (computer will just shut off). We've done a System Recovery. We've checked the motherboard, fans and sticks. We've done a Chkdsk (couldn't get the /r /p to run). I've run three memory tests on the RAM. I've run two Malware scans, I have a solid firewall and anti-virus program running.
Any advice? Seems to me that the only thing that I need to do is upgrade BIOS (I can't upload some of the drivers that I need without upgrading). Can I just upgrade to the latest version or do I have to do it one by one?

Thanks so much for putting up with my dummy question...

 

Thanks for responding...
I had my best friend (who's a computer tech and programmer) take a look into our system to find out what's going on. It has nothing to do with BIOS or SATA. We have a worm in our registry that wasn't taken out when we did the System Recovery (we didn't reformat the drive).
The issue was that randomly, the computer would just shut down then reboot and/or repeatedly shut down and reboot. There would be error messages instantly once Windows would run again and it would be from the same registry file. It didn't happen all of the time, just every once in a while during the day and after noon. There would be spurts of it, four or five shut downs at a time or it would just happen once. Also, our RAM is shot and needs replacement.
So, we are reformatting and reinstalling on Sunday.
I thank everyone at this site who has helped me for the past two weeks while I've tried to figure out the issue.
The downloads have been incredible and I'm so happy that I found this site.

 

Thank you for the links. We know the way that the worm got in. Our internet provider told me to unhook our wireless router about six or seven months ago (I was having some connectivity issues). That they really didn't like the fact that we were even using one. Last time I listen to them...
Yes, we are doing a full and entire reformat of the entire drive (no partitions- wiping it clean and reprogramming it with Linux). Which is kind of cool, because my best friend lives in Germany and I have to physically do all of the work myself. So, I'll get to learn some programming and coding which has been absolutely fascinating to me for the past ten days.
When we did the initial Recover, no one told us that we had to reformat the disk. And that was from two people that I used to really trust their knowledge.
Anyway, this site is the absolute best in the world and I love that all of the pros are really nice and courteous to the rest of us.