Do not acept more tham four 2 GB ddr2 module

RAM / Max RAM Up to 1 GB of DDR2 533 MHz memory, upgradeable to
2 GB using two soDIMM modules (dual-channel support) RAM / Max RAM Up to 1 GB of DDR2 533 MHz memory, upgradeable to
2 GB using two soDIMM modules (dual-channel support) RAM / Max RAM Up to 1 GB of DDR2 533 MHz memory, upgradeable to
2 GB using two soDIMM modules (dual-channel support) RAM / Max RAM Up to 1 GB of DDR2 533 MHz memory, upgradeable to
2 GB using two soDIMM modules (dual-channel support)Max RAM: Up to 1 GB of DDR2 533 MHz memory, upgradeable to
2 GB using two soDIMM modules (dual-channel support) This is the kind of memory you need, no matters the branch

Your laptop's RAM is upgradeable to up to 4 GB using two DDR2 533/667 MHz SODIMM modules.

So your upgrade options here are:
1. Buy a 1 GB DDR2 533/667 MHz SODIMM module & install it to get a total RAM of 2 GB (Price around US$ 25).
2. Buy a 2 GB DDR2 533/667 MHz SODIMM module & install it to get a total RAM of 3 GB (Price around US$ 45).

You need the EXACT speed rated RAM.
Your support page states it needs.....
400-MHz DDR2 SDRAM
NOTE: Your computer supports only registered memory

Memory capacities
256-MB, 512-MB, 1-GB, 2-GB, and 4-GB ECC

256-MB, 512-MB, 1-GB, 2-GB, and 4-GB ECC modules to a max of 16GB
more info here
http://support.dell.com/support/edocs/systems/ws470/en/ug_en/about.htm

max ram per slot is 1gb, for 2GB total. A 2 GB module will not work

http://www.crucial.com/store/listparts.aspx?model=Aspire%204315

Definitely not. Dual channel technology requires that the 2 RAM modules installed in each bank be of the same capacity, data rate, & even better be from the same manufacturer.

eMachines T3642 Computer takes the PC2-5300 DDR2 SDRAM DIMMs. Supports Dual Channel DDR2. Memory Type, and comes installed with 1.0 GB = 512 MB (removable) + 512 MB (removable) of Memory. You can upgrade your eMachines eMachines T3642 Computer to up to a maximum of 2.0 GB Memory, the system has 2 sockets to install Memory, already with 1.0 GB = 512 MB (removable) + 512 MB (removable) standard Memory installed. For best Computer performance use the maximum amount of allowed Memory per slot for your Computer.


INSTALLATION PROCEDURE
1. Place the computer power switch in the "off " position and disconnect the AC power cord.
2. Remove the computer top cover following the instructions in the model-specific owner manual.
3. Before touching any electronic components, make sure you first touch an unpainted, grounded metal object to discharge any static electricity stored on your clothing or body.
4. Locate the memory expansion sockets on the computer motherboard. If all the sockets are full, remove smaller capacity modules to allow room for higher capacity modules.
5. The ejector tabs shown in the illustration are used to remove a module. By pushing outward on the ejector tabs, the module will pop-up from the socket and it can then be removed.
6. Handle your new module carefully; do not flex or bend the module. Always grasp the module by its edges.
7. For most installations, DDR modules can be installed in any available expansion slot. Other installations may require the memory to be installed in a particular sequence based on the modules capacity. Check your owner manual to determine the correct installation sequence for your configuration.

Insert the module into an available expansion socket. Note how the module is keyed to the socket. This ensures the module can be plugged into the socket one way only. Firmly press the module into position, making certain the module is completely seated in the socket. The ejector tabs at each end of the socket will automatically snap into the locked position. Repeat this procedure for any additional modules you are installing. 8. Once the module or modules have been installed, the computer top cover can be reinstalled.
9. Plug in the AC power cord and reinstall any cables disconnected during the installation process.
10. Turn on the computer and follow the instructions in your computer owner manual that describe the steps necessary to allow your computer to recognize the newly installed memory.

I’m happy to help further over the phone at https://www.6ya.com/expert/william_83fc156eee2b555e

According to the specs of this laptop model, it supports up to 4 GB of DDR2 533/667 MHz memory using two soDIMM modules. This means that you will have to replace the 512 MB memory module already installed in your laptop, & replace it with 2 soDIMM DDR2 533/667 MHz memory modules, each of 2 GB capacity.

Look closely at the BOLD print

Memory Upgrade for eMachines eMachines T5082 Computer, the eMachines eMachines T5082 Computer takes the PC2-4200 DDR2 SDRAM DIMMs. Supports Dual Channel DDR2. Memory Type, and comes installed with 512 MB (removable) of Memory. You can upgrade your eMachines eMachines T5082 Computer to up to a maximum of 2.0 GB Memory, the system has 2 sockets to install Memory, already with 512 MB (removable) standard Memory installed. For best Computer performance use the maximum amount of allowed Memory per slot for your Computer.
Choose the following Memory Upgrade for eMachines eMachines T5082 Computer.

CHECK RAM ONE BY ONE, IT MAY BE POSSIBLE THAT THE RAM IS FAULTY

I had the same issue on this board where it came with a Samsung 512 MB 533 MHz PC2-4200 DDR2 DIMM. I put in a 1 GB Kingston with the same specs (533 MHz PC2-4200 DDR2) and it would not recongize the Samsung anymore with the system reading as 1 GB of RAM instead of 1.5 GB. Tried every configuration and would only see the Kingston. It would only see the Samsung if I pulled out the Kingston regarless of the slots I use. So, I just bought the exact same make/model of Kingston and it recognized that fine and the system now has 2 GB of memory (max this board allows). And, I had already installed the latest BIOS for this board from Intel before doing all this so wasn't an old BIOS. I'm figuring the board didn't like something about the Samsung memory (speed, module configuration, etc.) that made it not play nice with the Kingston. If interested I bought the DM8400A/1G Kingston modules. And, this board appears not to support dual channel memory. Only has channel A, slots 0 and 1, and I read need two channels to support dual channel (seems obvious). Boards that supports dual channel memory normally have 4 memory slots, two for channel A and two for channel B, then put in matching modules in slot 0 for channel A and B and have dual channel memory access. And if want more ram, then matching modules in slot 1 for channel A and B.