If it's a windows PC then it could be a keyboard problem, try and clean the keyboard as best as you can. For example I'd tip it upside down, then clean it with a hoover and being a bit more confident on my separate PC keyboard I'd also pop a few keys off and give it a good clean underneath.
What sort of computer is it? Is it a Mac or is it a Windows PC? The beeps can sometimes give a bit of information as to what is going on, so when exactly do they occur and what's on screen at the time?
I think you'll need to get in touch with Dell. Different Dell models have different beep codes. I think Dell offers free email support but charges for telephone support. Have a look on Dell Support. You'll need your Dell Service Tag (an id code that will be on a sticker on the base of your laptop) and then tell them of the beeps that are happening on start-up. They'll probably ask you to run the diagnostics so if you've already done that and it didn't say anything useful then tell them that as well.