This link...
http://www.techspot.com/community/topics/the-complete-bios-beep-guide.95391/
Suggests that a Keyboard controller has failed but that may only be for some machines - yours may be different. - Preliminary and rudimentary tests from the BIOS chip before attempting to load the Operating System.
Use Google and search for Dell ??? 6 beeps where ??? is your specific machine.
If it does come down to a new machine a Low Specification Laptop can be yours for about £300 - there is no need to pay more - there is no need for super fast performance or big disk and massive memory.
Good luck...
Peccavi
March 2013