BLACK SCREEN BEEPS 6 TIMES

Please read this:

DELL BEEP CODES
Beep Codes Beep Code Description Failure Coverage 1 System Board: BIOS ROM failure System Board, covers BIOS corruption or ROM error 2 Memory No Memory / RAM detected 3 Chipset Error (North and South Bridge Chipset DMA/IMR/ Timer Error for Intel platform); Chipset Error System Board Chipset Failure Time-Of-Day Clock test failure. Gate A20 failure Super I/O chip failure Keyboard controller test failure. 4 RAM Read/Write failure Memory failure 5 RTC Power Fail. CMOS battery failure 6 Video BIOS Test Failure Video card / chip failure 7 CPU Cache Test Failure CPU failure 8 LCD LCD failure

DELL BEEP CODES
Beep Codes Beep Code Description Failure Coverage 1 System Board: BIOS ROM failure System Board, covers BIOS corruption or ROM error 2 Memory No Memory / RAM detected 3 Chipset Error (North and South Bridge Chipset DMA/IMR/ Timer Error for Intel platform); Chipset Error System Board Chipset Failure Time-Of-Day Clock test failure. Gate A20 failure Super I/O chip failure Keyboard controller test failure. 4 RAM Read/Write failure Memory failure 5 RTC Power Fail. CMOS battery failure 6 Video BIOS Test Failure Video card / chip failure 7 CPU Cache Test Failure CPU failure 8 LCD LCD failure

Since you have video with an external monitor your lcd panel is going out.This is not hard to repair only costlyhttp://www.insidemylaptop.com/remove-lcd-screen-replace-inverter-board-acer-aspire-5100-laptop/

if you need your laptop always in ready use change the time your computer is on in control panel then log off your device will be on always until you shut it down it constantly drains battery
There is a way to fix this try reinstalling windows
or just take it to software mechanic

Is is possible that the RAM you put in was not sited properly. Just check it to see if it is right. You might need to troubleshoot by removing one peripheral at a time. Try removing the keyboard, and turn it on and see what happen. If same, mouse, network card, etc until you find the issue.

This sounds like a hard drive is, or has failed. Either that or the RAM (memory has gone bad)
Did you let the laptop overheat? Was it left on for a long time? Or is this just an old machine ?
I would replace the hard drive, and reload the operating system, that is if you really want to keep the laptop. If that solves it great! Also, did you notice if there are any "beep" noises, or error messages when it acts up? Often times, you can go on the internet and find out what the messages mean.

Heres one solution that I found. If your ps3 turns on but does not boot up just stays a black screen most likely the hard drive got corrupted. So unfortunately you will lose all your saves. But to save the system when you power on the ps3 hold the button down its should beep once keep holding it and it should turn red in standby mode. Keep holding the power button down though. It should turn green again keep holding it should beep then double beep this time instead of going into standby. Let go now and some options will come onto the screen. You will need to plug in your ps3 controller and 6 options should come up. Reformat PS3 worked for me but I lost all my saves. Good luck!

RESTART IN SAFE MODE.
OR
REBOOT SYSTEM, BEFORE IT BOOTS PRESS
F6 UNTIL YOU HEAR THE BEEPING NOISE, THAN STOP AND SELECT SAFE MODE
THAN CONTROL PANEL AND SELECT POWER OPTIONS
POWER BUTTON OPTIONS

The bios beep codes indicate the video card is not working, so you won't see anything on the screen.

Your video card is either dead, or is not contacting the board correctly.
If you are keen to open it up I will offer instructions to assist you. But in reality, your safest bet is to take it to a laptop shop and get them to do it. There are a lot of tiny screws in these things.

This could be an overheating processor problem,dependant on the motherboard and what the beeps mean. The fan speeds up to cool it down, there may be dust collected in the heatsink on top of the processor, check it and gently brush off dust. Check that the vents on the side are atleast 6 inches clear of anything for good circulation. To see if it is an overheating thing, remove both sides of pc and run it in an open space to see if the same thing happens. While you have the side off just check your memory and other peripheral cards are all seated correctly and not loose.