Memory Connector Failure

My son's E520, Win7HP (originally Vista, then clean custom installed
Win7HP using Win7 Upgrade DVD in Nov. 2010...all legit) , 2GB RAM, had
been intermittently going blue screen with memory dumps scrolling down
the screen, for about a week.  Last night, it was more or less continuous
on every reboot.

The front panel diagnostic lights, page 47 of the Owner's Manual, did not
show any problems.

Owner's Manual:
http://support.dell.com/support/edocs/systems/dime520/en/OM_en/NH730A01.pdf

A Safe Mode boot worked intermittently, but would crash in a minute or so
after reaching the desktop.  I finally got a stable desktop with a normal
boot, and put the Win7 Upgrade DVD in the DVD drive.  I ran setup.exe
from that drive, and did a custom install of Win7.  The machine even
spent an hour doing Window Updates, and started to work fine again, no
crashes.  But ten minutes later, memory dumps began.

Now, a 1-3 diagnostic front panel light combination appeared, and
indicated "Memory modules are detected, but a memory configuration or
compatibility error has occurred"

Memory connectors 1 and 3 are occupied with the original dell shipped 1GB
RAM sticks each, totaling 2GB.  In the picture on page 68, these are the
memory connectors with the white connecting tabs.

Per page 68:
http://support.dell.com/support/edocs/systems/dime520/en/OM_en/NH730A01.pdf

I removed one stick at a time, and each one worked independantly in
connector 1.  If I installed both, one in 1, and one in 3, I got the 1-3
error lights.  This indicated to me that the memory modules were ok, but
the memory connector 3 was bad.

Question:
Do memory connectors 1 and 3, both, have to be occupied before installing
any memory in connectors 2 and 4?  I could have just tried last night,
but didn't think of this until now.

Any other comments?