My comp is randomly crashing

I have an older Dell comp that is running Windows XP version 5.1.2600. It seems to be crashing randomly. I have been combing over the event logs and can't really pin point what is happening. I have received 2 different sets of error codes. Is there a site where I can find out what these numbers refer to? I am pretty decent at trouble shooting but other than thinking the power supply might be going I am stuck. I would appreciate any advice. Thanks!

Error code 1:

BCCODE: 1000007e
BCP1: C0000005
BCP2: F7B77343
BCP3:F78CEB38
BCP4: F78CE834
OSVer:5_1_2600
SP:3_0
Product: 256_1

Error code 2

BCCODE: 10000050
BCP!: FFFBFFF8
BCP2: 00000000
BCP3: 80551211
BCP4: 00000000
OSVer: 5_1_2600

Go here and post the results of the memory and hard drive tests:
http://www.techspot.com/vb/topic51365.html

Learn how to attach any minidumps you find. You may have to zip them to attach them properly. Also, make sure that the insides are clean and that all fans are free from dust and spinning normally