Hp desktop starts up fine but monitor goes to sleep, then the CPU will start beeping 2 beeps

SOURCE: no display no beeps but cpu is fine,power led is on and fans are running

Have you upgraded the memory?

SOURCE: HP AMD Desktop beep noise

HP BIOS beep codes
http://welcome.hp.com/country/us/eng/support.html
Because Hewlett-Packard (HP) uses a variety of motherboards and BIOSs, their computers use a variety of beep codes. Instead of listing each model's beep codes, links are provided to the support pages of several popular Hewlett-Packard desktops.
Note: Hewlett-Packard and Compaq merged in 2002 and the new company dropped the Compaq name from all but a few consumer product lines--such as Presario desktops and notebooks. This table lists only HP-branded desktops, while the next table lists Compaq-branded machines.
Model
System codes and messages link
e-PC c10/s10
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=tis13707
Kayak
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=tis06334
Kayak XM600
http://h20000.www2.hp.com/bc/docs/support/SupportManual/lpv07804/lpv07804.pdf
Kayak XU800
http://h20000.www2.hp.com/bc/docs/support/SupportManual/lpv07804/lpv07804.pdf
HP Multimedia PC series
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=bph01686
Pavilion Desktops with Phoenix BIOS
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=bph07107
Pavilion 5010, 5030, and 5040
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=bph01004
Pavilion 7xxx (7010, 7020, 7030, 7050, and possibly others)
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=bph01053
Vectra PCs with Phoenix BIOS (VL4, VL5, VL7, VL8, VLi8, VE2, VE3, VEi7, XM4, XA5, and possibly others)
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=bpv03305
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=tis06108
e-Vectra
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=tis06446
Vectra VE 5/xxx Series 4
http://h200004.www2.hp.com/bc/docs/support/SupportManual/bpv03974/bpv03974.pdf
Vectra VL600
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=tis01866
Vectra XA5
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=tis06112
Vectra XA 5/XXX
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=bpv03314
Vectra XE310
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=tis13051
Workstation i2000
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=tis07621
Workstation xw3100
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=c00038866


Compaq (Hewlett-Packard)
http://h10025.www1.hp.com/ewfrf/wc/siteHomeC?lc=en&cc=us
Because Compaq uses a variety of motherboards and BIOSs, their computers use a variety of beep codes. Instead of listing each model's beep codes, links are provided to support documentation for several popular Compaq desktops.
Note: Hewlett-Packard and Compaq merged in 2002 and the new company dropped the Compaq name from all but a few consumer product lines--such as Presario desktops and notebooks. Official Compaq support documentation is difficult to find on HPs Web site.
Model
System codes and messages link
Business Desktop d330 and d530
http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=c00274415
Multiple Models
http://forums1.itrc.hp.com/service/forums/questionanswer.do?admit=716493758+1107879885254+28353475&threadId=222666

SOURCE: 2 beeps on HP Pavilion a1600n

It all depends on your bios type.  Here is some more information for you to reveiw. http://en.kioskea.net/contents/pc/bios.php3

SOURCE: Delay in Monitor display once the system goes in sleep mode

Instead of sleep mode, tyr hibernate. It is generally faster except the whole computer shuts down. When you power back up, you're exactly where you were. Mine takes about 30 seconds.

SOURCE: cpu says no input vga signal, then goes to sleep

The no input VGA signal just means that the monitor is not receiving anything from the graphic card on the tower. Is the card a digital (DVI) output card? You'll know by the connector, it's white and slightly wider than a standard VGA connector. If so, perhaps the monitor is set to the wrong input?

If that isn't the case, and the computer is using an on-board or built-in graphics controller, you could try resetting the system's CMOS settings by setting the clear-settings jumper on the system board, or simply remove the plug and CMOS battery for a few minutes. Check the computer's documentation on the exact steps to do this.

Hope this helps!