New RAM does not work

Hi.
I went through posts here but still struggle to get mine working. I have decided to upgrade my old PC a bit. This is what I have:
CPU: Intel Core2Duo E6700 @2.67Mhz
Mobo: P-965 NEO
system: Win 10 Pro 64-bit
GPU: DDR2 512MB some N-vidia
Now my mobo accepts 800Mhz max, 1.8Voltage, 4-slots, max 8GB of RAM. 2 slots taken, two empty.
RAM: 2x2GB DDR2 800Mhz running in dual mode (shown as well during Win startup - it says dual mode, 800MHz). This is what I see in CPU-Z:
SPD PART:
PC2-6400 (400Mhz)
Manufacturer: Kingston
Part Number:99U5429-007.A00LF
Serial nbr:67363CE3
JEDEC 1: 4.0, 4, 4, 12, 16...266MHz
JEDEC 2: 5.0, 5, 5, 15, 20...333MHz
JEDEC 3: 6.0, 6, 6, 18, 24...400MHz

MEMORY PART of CPU-Z:
TYPE - DDR2, Size: 4GB, Channel: Dual, DC Mode: Symmetric
DRAM freq: 399.3Mhz
FBS : DRAM: 2:3
CL = 6
tRDC = 6
tRP = 6
tRAS = 18
CR = 2T

Now I bought 2x2GB sticks of the following DDR2 RAM:
2GB Module - DDR2 800MHz, Part Number: KVR800D2N6/2G, Specs: DDR2 , 800MHz , Non-ECC , CL6 , 1.8V , Unbuffered. More info to be seen:
http://www.kingston.com/en/memory/search/?partid=kvr800d2n6/2g
Both are Kingston, both are 800Mhz, both are 128M x 8, both are 1.8V.
The ones inserted are: 99U5429-007.A00LF
The ones I can't insert: 99P5429-006.A00LF - as written on the sticks
Notice the diff only in letter U vs P and 007 vs 006. I don't know what it means.

Now what does it do: when I took out all the RAM and insert the new one, to any of the slots (tried all 4) - system won't start - black screen - can't get to BIOS either. I keep the dual channels sticks on, insert this new RAM - same story. System won't start, black screen, can't get to BIOS.
I put back the 2x2GB which are working - system starts normally. I checked the BIOS - I have everything on AUTO, that is:
DRAM timing: AUTO. If I put this to MANUAL, I open other possibilities, such as:
CAS Latency (Tcl)
RAS to CAS delay (Trcd)
RAS precharge time (Trp)
Min RAS active time (Tras)
In these options I can set the numbers manually, but I don't know what that is so kept that on automatic.
MEMORY HOLE = disabled

I also have a 1GB stick (some no name, label on stick says 800Mhz, 1GB). My system starts up with this stick, system says 5GB RAM but only 667Mhz (I don't know why). Checking this 1GB stick in CPU-Z I get no manufacturer and JEDEC 1,2,3 is lower - I suppose this stick is of a lower quality, not 800Mhz (?) and my system reads it though, sums to 5GB, but takes only 667MHz.
System starts up even with this 1GB stick only. Again, I put aside any of the new sticks - no luck.

Any idea what am I missing in running these new 2x2GB RAM sticks? I tried both of them, all slots - no luck. Both of them together, alone...etc... I was thinking that both of them are corrupted, but even if I put them with my 4GB working sticks, the system just won't run. I'd expect it'd run but not take this one into account...

Thanks a lot for any help!