You’ll notice that the RAM is being run at half the speed expected. This, plus the fact that you are seeing four logical slots but only two physical ones points to the problem being due to the sided-ness of the RAM. The RAM stick you have is likely double-sided, so the system is seeing two sticks instead of one (note, the sided-ness does not refer to the physical location of the chips).
Like most things in life, double-sided RAM has its pros and cons. On the one hand, it allows you to have more memory in fewer slots and at a cheaper price than single-sided RAM of the same size. On the other hand, only one side can be accessed at a time, which usually reduces the effective speed of the “two” sticks as a whole as opposed to two sticks of single-sided RAM (or one stick of single-sided, double-size RAM). It should not normally be half the speed, but perhaps that memory controller happens to be designed that way.
I’d have recommended check the BIOS to see if the memory-CPU speeds are set to auto, but there does not seem to be any such options (laptops usually limit such settings).
If you can get single-sided RAM instead, I suspect that the speed would be back to 1333MHz.
Your motherboard does indeed support DDR3 RAM at up to 1333MHz, so you would be fine getting DDR3 RAM up to that speed.
PC3-10700 and runs at up to the maximum speed that your motherboards supports (1333MHz).
If you had more than one stick of RAM, then what would likely be happening is that you have mixed and matched the RAM sticks in your system, so your fastest RAM is being throttled down to a speed that is compatible with your slowest RAM stick. Check the other sticks in the Slot Selection drop-down box.
If you remove the slower RAM stick(s), then your motherboard should be able to run the faster RAM at full-speed (though you may need to update the BIOS to make sure it has detected the new RAM).
If you only have one stick though, then something is going on since that stick should support 1333MHz as should your motherboard. Assuming that neither component is defective, then you need to examine the settings in the BIOS since something in there is probably causing it to run slower (you shouldn’t have to do anything; it should be automatic):
From page 63 from the manual:
Additional memory will increase application performance by decreasing hard disk access. Visit an authorized service center or retailer for information on memory upgrades for your Notebook PC. Only purchase expansion modules from authorized retailers of this Notebook PC to ensure maximum compatibility and reliability. The BIOS automatically detects the amount of memory in the system and configures CMOS accordingly during the POST (Power-On-Self-Test) process. There is no hardware or software (including BIOS) setup required after the memory is installed.
First check your temperatures (e.g., with SpeedFan) to see if it is being throttled due to heat. Then, try loading your BIOS’ default settings and saving (note down the existing settings first). Also check for any turbo or boost settings that could affect it (though page A-12 of the manual indicates that it shouldn’t have any such features).