To do a hardware test, you insert the OS X install discs and boot off it by holding the "d" key as the comuter starts up. The crashing can be caused by bad memory, running low on memory and your programs are trying to create virtual memory space in logical memory that doesn't exist, bad OS X install, permission issues, or hard drive corruption. There are other possibilities but these are the most likely causes. By upgrading to two gigs, you would bypass a memory defect and deficit all together.