Removing cover on gateway 300

It should be the same as the video.

https://www.google.com/search?q=Gateway+ZX4270+how+to+add+memory

and here

https://www.google.com/search?q=gateway+zx4270+hard+drive+replacement

....

fix laptops for a living, at the cost of ordering and replacing, your better off replacing the entire thing or seeing how much gateway will charge. Best cost I can get is $179 and Id charge at least $100 to put it in...thats 300 after tax, and those new with maxed out memory are going for 500 bucks

You should only need to unscrew one. http://support.gateway.com/s/notebook/2009/gateway/lt/lt20/LT20faq5.shtml

20-60 Dollars
A great site to buy from is HERE
NOTE: all these power supplies will work for your computer, you may want to pay attention to the dimensions though

This netbook is really the Acer Aspire One D255. You have to pop off the keyboard, then remove 4 screws that hold the back panel in place, which will allow you to remove that back panel in order to get to the memory.

Here's a video - blurry but it tells the story: http://www.youtube.com/watch?v=6KYNTvF0-5M

Computer has three short beeps as it starts? computer RAM (memory) related issue.

If you've recently added or tried to add additional memory to the computer and have started getting these beeps. Remove all new memory you've added to the computer. If the computer works fine after removing the new memory you're encountering either an incompatibility or defective new memory.

Sometimes when the computer is moved and/or over time a memory stick can become loose causing the computer to be unable to read the memory or get errors as it's reading it. Try fixing this issue by opening the computer removing each of the memory sticks you have in the computer and then placing them back into the computer.

Hope this helps.

The first place i would look -- check the new memory, make sure its the correct type and voltage for your motherboard. Next, check to make sure your ram are both the same speed, voltage , etc. some motherboards are picky about memory types and some require that paired memory be installed.
Reseat (remove and replace) the memory in it's slot, poorly seated memory can cause restarts or no-starts. try these and post again here if you need further assistance.
Regards

Head to www.crucial.com. Click the "Scan My System" button and allow the ActiveX controls to install. They will scan your computer and tell you how much memory you have, the maximum your system can take, and will price memory you can order from them. It will also tell you what type of memory you have as well as speed.

Upgrading RAM on your Gateway 700X (DDR) Computer is easy, Gateway 700X (DDR) Computer takes the PC3200 DDR SDRAM DIMMs. Supports Dual Channel DDR. RAM Type, and comes installed with 512 MB (removable) of RAM.
You can upgrade your Gateway 700X (DDR) Computer to up to a maximum of 2.0 GB RAM, the Computer has 4 sockets to install RAM, already with 512 MB (removable) standard RAM installed. For best Computer performance use the maximum amount of allowed RAM per slot for your system.

I was initially confused about the addition of the Dell laptop in the plot before realizing what you are saying:

I think its your RAM. Did you ground yourself while removing or replacing the ram to prevent static shock from damaging the device or memory sticks?

If not, try getting another 512 stick (pretty cheap) from best buy for your gateway and testing it out. Save the receipt.

Also, post the model of your gateway laptop as some computers can not handle large amounts of ram. Most will only allow up to 2x the original amount.