We've had the exact same question about the older Intel socket 775 motherboards in the past. Although your motherboard has SATA 2 3Gb/s capabilities it might also depend on whether or nor the motherboard's System BIOS can be switched from IDE mode to AHCI mode. Some of the really really old socket 775 boards do not support AHCI mode.
Turn off your pc. Start the pc and immediately go into the System BIOS. Check to see if there is some sort of setting somewhere that allows you to change from IDE mode to AHCI mode. Don't actually change it. Just see if the setting is available. Let us know what you discovered.
There should be 4 SATA headers (connectors) on your motherboard. Your current hard drive is plugged into one. You optical/dvd/cd drive should be plugged into a second one. Just follow the cables from the devices to the motherboard. There should be two unused SATA headers and all 4 headers are probably the same color. Let us know if one is a different color.
If it is in fact an lx4710 model then you may have another problem. According to the specs in the link you provided the motherboard is only SATA capable rather than SATA 2 capable. That conflicts with the pc over at newegg that you linked to in your original post. Don't know which is correct.
If that is the case then it would be simpler and easier to just purchase an inexpensive socket 775 motherboard that has SATA 2 capabilities. They typically cost between $40.00 and $50.00. Here is link to 27 boards over at newegg:
Switching the MB on a system is a much more complicated task then switching a boot drive, esp in something that is a prebuilt system.
Is there a reason not to run that drive on a Sata 1 port? He would still get a very noticeable performance jump imo even runnng at Sata 1 speeds. I was just going by the newegg link as you mentioned, didn't look far enough into the board etc.
tomatthe - Yes, swapping out a motherboard would be a little more complicated but worth the $50.00. I mentioned it because there may be compatability issues between old boards, old chipsets, old controllers and new modern drives.
We won't know for certain until the OP posts additional information.
Iridionprime - OK! If you are positive about the pc, then it has SATA 2 3Gb/s capabilities. Now click on the following link and download the reference guide and installation manual for your pc:
EDIT / UPDATE - I checked reference material and specifications at several sites. The reason you were not able to see any available SATA headers (connectors) on the motherboard is because there are none. There are no additional SATA headers available for adding an ssd. The board is a low budget, basic, OEM board without any extra features and almost no expandability.
It now looks like your only available option is to purchase a new socket 775 motherboard for about $50.00. Other users have also had to do that and have been happy with the results.