upgrade motherboard on cq5814

[marpet33]

I have a Compaq Presario cq5814, I have already replaced the hard drive and power supply, can I replace the mother board to upgrade to better graphics card.

 

[C12Friedman]

There are drawbacks to what you are looking to do...
1) Replacing the motherboard will mean the Operating System will also need to be replaced since it is tied directly to the motherboard.
2) You will also need a new CPU since yours is soldered onto the motherboard (good idea anyway) and possibly ram which add some more expense
3) The HP case likely does not support a standard µ-ATX size motherboard (9.6" x 9.6") since your current board is a bit smaller at 9.6" x 6.8" so a little more expense for a case.
Assuming your new PSU is of decent quality and has enough power, here's what you're looking at to get a decent upgrade (not including whichever graphics card you decide on)

PCPartPicker part list / Price breakdown by merchant

CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($69.99 @ NCIX US)
Motherboard: ASRock FM2A88M PRO3+ Micro ATX FM2+ Motherboard ($48.98 @ Newegg)
Case: Enermax OSTROG ATX Mid Tower Case ($33.75 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 OEM (64-bit) ($86.75 @ OutletPC)
Total: $239.47
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-08 08:09 EDT-0400

Since you are looking to add a graphics card, I am assuming you are looking to game on this PC. We can advise better with an idea of the type of games you are looking to play including advising on graphics options. I just threw the list of parts together as an inexpensive example - not a recommendation of any nature