My tower turns on and makes this consistent beeping sound. And nothing shows on the screen.

The beep codes have nothing to do with dust, They usually signify a memory, video, etc. on the motherboard. The BOIS manufacturers (Phoenix, American Megatrends-AMI, IBM, etc.) have their own beeps codes. You can find them online by searching beep codes.

that is a BIOS error. 2 beeps means a post error one or more of the components is not working correctly.

ok cammy there are several ways to solve this puzzle of yours.... first off here is a link that will explain the multiple beeps from your computer as follows!

http://www.d-a-l.com/help/general-hardware-issues/12347-beep-code-list.html

and being that your computer beeps 6 times could possibly mean that

6 Beeps 8042 Gate A20 failure Bad CPU or Motherboard

Generally, six beeps means a keyboard controller error. Unplug and replug
your keyboard when computer is off. If that doesn't work, you may have a bad
controller on the motherboard .
Generally, six beeps means a keyboard controller error. Unplug and replug
your keyboard when computer is off. If that doesn't work, you may have a bad
controller on the motherboard .

Generally, six beeps means a keyboard controller error. Unplug and replug
your keyboard when computer is off. If that doesn't work, you may have a bad
controller on the motherboard .

Whenever you hear a system beep it means the system is hung due to a hardware error. How many beeps does it make? The number off beeps can help you dtermine what the issue may be. It could be a video card failure, cpu failure, ram failure, or even a power supply issue. The beeps aren't very specific but they can give you a starting point. Given that it is such a generic error code I would suggest taking the PC to a repair center. I wish I could be of more assistance. If you have any further questions please feel free to reply in this thread.

Quick question, did you upgrade any components prior to the error beeps?

If you added more memory this may make your tower beep.
If so I WOULD REMOVE THE ADDED MEMORY AND THEN RESTART

Here are the instructions for a cpu upgrade for COMAPQ PRESARIO 5WV257

http://h10025.www1.hp.com/ewfrf/wc/document?docname=bph07139&lc=en&cc=us&lang=&product=93917&dlc=#

Sounds like a hardware problem. Has the computer been moved recently? Check that all cards and cables are securely connected.

Here's a list of beep codes

As I can see the problem is not monitor but your PC if computer chasis beeping, depends on number of beeps the problem can be VGA card one long beep and 3 short or RAM if it beeping one by one short beep and finaly CPU if it continuosly beeps like police sirene. If beeps are pointing to VGA or RAM you must open computer chasis and plug out VGA and RAM and clean dust out of slots and of VGA card and RAM as well with painbrush and vacum cleaner and plug them back.
Good luck!

Clearly shows problem in deflection area both horizontal and vertical section. Horizontal lines is due to vertical section problem and making bbzzzz is due to horizontal output transistor short and sometimes LOT SHORT.

try a cheep video card from your local used computer parts store they're every where, you'll ask for a pci video card.