Suggest you remove the Ram Memory modules, ('Stick'), and clean the gold plated contact pins. Then reinstall.
The beeps you hear are BIOS Beep Codes. The computer's way of telling you something is wrong, and an area to look into for it.
2 short beeps indicate a memory problem.
The eMachines T6528 uses an MSI MS-7207 motherboard.
(Micro Star International)
Otherwise known as the MSI K8NGM2-FID /IL / L,http://www.msi.com/product/mb/K8NGM2-FID--IL--L.html
Uses DDR Sdram ram memory.
(Either 266MegaHertz, 333MHz, or 400MHz. Which is
PC-2100, PC-2700, and PC3200; respectively)http://en.wikipedia.org/wiki/File:Generic_DDR_Memory_%28Xytram%29.jpg
Handle the Ram Memory by the BODY. The Body is everywhere on the ram memory module, Except the gold plated contact pins at the Bottom.
The Body is coated with a see-through protective plastic.
Use a pencil eraser to clean the gold plated contact pins.
If you are using an eraser on the end of a pencil, and not a solid eraser; refrain from letting the metal band touch, the gold plated contact pins.
Rub across all contact pins, (BOTH sides), and up, and down on them. You don't have to use too much pressure.
Once finished use air to remove the eraser dust.
You can use a can of compressed air for computers, if available; or air pressure from your mouth will be sufficient.
(Humans can deliver up to 20 pounds of air pressure)
BEFORE you reach inside your computer, FOLLOW Anti-Static Precautions.
Your body carries Static electricity. Static WILL fry out (Short Circuit), the delicate hardware components inside a computer.
Relieve your body of Static.
Computer ON a table, computer unplugged from power, computer case open;
TOUCH an unpainted surface, of the metal frame of the open computer case.
This action will relieve your body of Static.
IF you leave your computer in the middle of working on it, be SURE to Touch the metal frame again upon your return.
Use a can, or two of compressed air for computers. You may wish to wear a dust mask also.
For additional questions please post in a Comment.
[If this doesn't 'cure' the problem, we will diagnose further ]