Here are
HP's specs for your machine. This is your motherboard.
You face several problems trying to install a new motherboard in your case:
1. Most motherboards used in "department store" packaged computers (HP, Dell, etc.) use a 9 pin header to connect to the front panel switches and LED's. It's in the lower right corner of the above pic. Most separate motherboards use a different arrangement for these front panel connections that anticipates separate wire pairs with independent 2 - 4 pin connectors.
Unless you find a motherboard with the 9 pin connector, to use your case, either you will have to find an after-market adapter (rare and expensive), or you will have to cut off the 9 pin connector from the front panel and attach independent connectors to each of the wire pairs to connect them to the new board. It can be done if you have soldering skills and you know what you're doing, but it's a lot of work. If you don't know how to do this, the money a qualified tech would probably charge would be better spent on a new system.
2. These same "department store" computers almost always include undersized power supplies. The one in your machine is only 250 watts, and it's several years old. It was barely adequate for its purpose when it was new, and you have no way of knowing how much longer it will last.
3. The cost of a genuine replacement motherboard from HP or eBay would be prohibitive. The license for Windows is attached to your machine so unless you replace the motherboard with another similar HP board that uses the same drivers and will accept your serial number, the copy of Windows in your CD/DVD recovery disk set will not install, and you will need a generic copy of Windows.
Sorry, but it isn't worth the cost or effort to ressurect an old, underpowered pile of components in need of a motherboard. If you can find an inexpensive motherboard that supports the AM2 CPU, the DDR2 RAM, you could salvage them and any plug-in cards (telco modem, etc.), and you'd have a reasonable machine for web surfing and light duty.
Your machine came with Vista, which isn't worth the effort to replace. If you go for it, get a copy of Win 7 and a motherboard that supports it.