Did you increase the default memory voltage in the bios?
Does it feel really hot?  Be sure to ground yourself before
touch-testing, carefully contacting only the epoxy part of
the chip and with very dry finger(s).  However, memory
overheating is not as likely as what I mention below, unless
the system were overclocked and the memory voltage was
manually increased.  On the other hand, one thing you might
try doing if the memory is at stock voltage still is to
raise the voltage one notch, then retest with memtest86+ to
see if this effects the error rate... if it has no effect at
all on the rate, return the memory to default voltage, but
if it does have a significant effect, you might consider
then retesting with the memory voltage raised another notch.
If your motherboard has fine increment voltage adjustments
this may be acceptible, but don't raise the memory voltage
very much, some would say 10% is a conservative maximum
especially without heat spreaders on the modules.

Most often, seeming instability with more modules simply
means the motherboard can't run so many stabily at the same
timings and/or bus speed.  Sometimes it is a matter of the
individual modules having too little margin and replacement
with higher spec'd modules will help.  Other times the
motherboard manufacturer will eventually release a bios that
uses more conservative timings with certain memory or more
modules installed.

For the time being, find out what your memory is spec'd to
use for timings.  Manually set those timings in the bios and
retest with memtest86+ (above you referred only to
"memtest86", be sure to try the "+" version).  If the
manually set timings don't work stabily, try increasing the
timings numbers.  More detail on memory timing settings can
be found with a google search.

If you find it unacceptible to have to suffer a (typically
single-digit percentage memory-)  performance degradation
from using higher timings, what remains is seeking a newer
bios for your motherboard that claims to address *someone's*
memory stability (even a different module, might reflect an
improvement with your modules), or returning the memory for
refund (it is not so likely to make a difference to exchange
the modules you have for the exact same replacement Kingston
modules in general, although rarely Kingston does use
different chips on different modules having the same
Kingston part #).

Unfortunately, if you have ran the system all the while with
the current instable memory configuation, including
installing the operating system(s), it is quite possible you
have some file corruption that could result in the system
remaining instable, and/or data corruption of anything
written to the HDD later, so after you have regained memory
stability it would be prudent to do a clean installation of
the OS again and if you can, abandon any data created (if
stored on another device not subject to corruption from this
instable system, abandon the copy of the data on this system
and restore the data from the other source).

Bump up Vdimm and try again with memtest86+. Just do a couple passes,
to determine whether the occasional errors are gone.

The real test though, will be with Orthos.

http://sp2004.fre3.com/beta/beta2.htm

   Paul