Difference between 1066 vs 10666 DDR3 Ram

It means that RAM labeled 1066 has a peak bandwidth of 1066 Mbps and RAM labeled 10666 has a peak bandwidth of 10666 Mbps.

The below taken from: http://www.tomshardware.com/reviews/ddr3-1333-speed-latency-shootout,1754.html

What's In A Name?
The "official" name for DDR memory is based on its bandwidth rather than clock speed. The easy method to convert data rate to bandwidth is to multiply by eight. Thus, DDR-400 is called PC-3200; DDR2-800 is called PC2-6400 and DDR3-1600 is called PC2-12800.
The math behind this conversion factor is simple: PC memory modules based on SDRAM technology use a 64-bit connection; there are eight bits in a byte and 64 bits equal eight bytes. For example, DDR2-800 transfers 800 megabits per pathway per second; its 64 pathways provide one eight-byte transfer per cycle and 800 times eight is 6400.
The problem comes with "rounding" and was first noticed with DDR-266 (PC-2100). The data rate of 266 MHz is actually 266.6 (continuously repeating decimal) megahertz, so the true transfer rate was 2133 MHz.
Today's DDR3-1333 has a peak bandwidth of 10666 MHz, which can be improperly rounded down and called PC3-10600, rounded up to be called PC3-10700 or stated without rounding as PC3-10666 depending on the manufacturer's desires.
Buyers will find that searching some venders for multiple DDR3-1333 brands will require them to check all three "ratings" to view modules of the same actual speed, but most brands label their DDR3-1333 products as either PC3-10600 or PC3-10666.

BuxunloX thanks for the explaination.

jamietoner: you're more on track with what I need.  I received (2) 4MG modules from one pack.  One worked (was recognized) one didn't.  It got all screwy when I tried mixing modules (1 + 4 ) (4+4) etc... in all the combinations I could think of.  So we got  (2) move 4GB sticks and tried all combinations of 4's we could think of (3) 4gb in slots 1,3,5  no good.  (3) gb in slots 2,,4,6 no good.  (4) 4gb in 1,2,3,5 etc.

I want to order Memory that will work and would like to end up with about 12 GB.  (6) 2GB seems limiting as I wont be able to add on without throwing away 2GB each slot.

The i7 -920, 2.66, 8MB, Bloomfeld, Co processor supports (NOW) Dual-in line 1GB, 1066, 128X64, 8, 240, 1RX8 sticks.       WHAT CAN I BUY?

Further, maybe I did receive ECC - I thought it was non-ECC but, that could explain the strange results.

MORE:  This is what I received

2 packages of:  
OCZ Technology Gold Series PC3-10666 8 GB (2 x 4 GB) Low  Voltage Dual Channel Kits OCZ3G1333LV8GK                by OCZ                

1333MHz DDR3, 1.65Volts
CL 9-9-920 (CAS-TRCD-TRP-TRAS), 240 Pin DIMM
Unbuffered
Gold Layered Z3 XTC Heatspreader
Optimized for P55, H55 and H57 Chipsets

That ram is non-ecc. Try each stick 1 at a time in slot 1(blue connector), the second closest connector to the processor. then when you get 3 known to work install them it slots 1,3,5. If that doesn't work then there must be some sort of compatibility issue, and you may want to see if there is a bios update available for the system.
More info on memory installation for your system.
http://support.dell.com/support/edocs/systems/435T/en/SM/memory.htm#wp1188716

You hit the nail onthe head saying that the computer uses TRIPLE CHANNEL MEMORY.  But, what I (and DELL) didn't know was that I couldn't use DOUBLE CHANNEL MEMORY in the computer.  At least this seems to be what the problem was.  I'll know for certain tomorrow when the Tripple Channel Memory arrives.  I had read that there is no difference between single/double/tripple memory.   That now appears false.  (We'll see).    THANKS