Usually I don't like hotlinking, but you can try the mirrors on this page. I am sure one of these mirrors allows you to download Aida.
http://www.majorgeeks.com/download181.html
Once you downloaded Aida, look into Motherboard->SPD. There will be the Serial Presence Detect EEPROMs information of the RAM modules. Very important for further investigation.
this is an example of my system memory (so you know how the information looks like)
Memory Module Properties
Module Name MDT512M PC400 CL2.
Serial Number 2B2A2007h
Manufacture Date Week 40 / 2004
Module Size 512 MB (1 rows, 4 banks)
Module Type Unbuffered
Memory Type DDR SDRAM
Memory Speed PC3200 (200 MHz)
Module Width 64 bit
Module Voltage SSTL 2.5
Error Detection Method None
Refresh Rate Reduced (7.8 us), Self-Refresh
Highest CAS Latency 2.5 (5.0 ns @ 200 MHz)
2nd Highest CAS Latency 2.0 (6.0 ns @ 166 MHz)
Memory Module Features
Early RAS# Precharge Not Supported
Auto-Precharge Not Supported
Precharge All Not Supported
Write1/Read Burst Not Supported
Buffered Address/Control Inputs Not Supported
Registered Address/Control Inputs Not Supported
On-Card PLL (Clock) Not Supported
Buffered DQMB Inputs Not Supported
Registered DQMB Inputs Not Supported
Differential Clock Input Supported
Redundant Row Address Not Supported
Another interesting read will be Motherboard->Motherboard. If you have an onboard graphics card, it should be listed there. At least the exact ID of the board is provided, which helps too. Well I wish you success for this.
To answer your concern if the RAM and the hdd are responsible for the instabilities....
At the moment its very propably your RAM, since the Video you send me of memtest86 had these red error prints (bit errors). Also it appeared (I could not clearly identify) that memtest recognized 584Mbyte of RAM. Which is a pretty odd number. You said you have 720 Mbyte RAM and an 128 vga. Lets assume your 720 is actually 768Mbyte. Lets further assume that the vga maybe uses 100% shared memory (means all the 128Mbyte). Then 768-128 = 640. Since 640 is not equal to 584, there must be a serious problem somewhere.
Your hdd is innocent until proven guilty (so lets assume it is okay for now). Once the RAM problem is fixed, and if there are still problems then, we can re-evaluate the situation. (atm. one cannot know if the RAM is masking errors... because every processed data is propagated to/from the RAM)