Amazon.com had 2 hp btx am2 boards a few days ago, but they either sold out or were removed. They are the only ones I've seen. Newegg has a rosewill atx case for only $24.99 with free shipping in their 48 hour sale beginning today. The link is at fatwallet. Then you can use a cheap micro atx board. They run about $45 shipped. Newegg has an ecs model with free shipping and a $12 rebate.
Is there a BTX Socket AM2+ Motherboard? If so, could you find me a BTX Socket AM2+ Motherboard.
BTX is a dead end. It was introduced by INTEL a few years ago. The only reason for buying a BTX motherboard is to keep a computer going if you do not have the money to buy a new case. If the chipset is not the same as the one you are replacing you will have to re-install the OS and if you do not have the CDs to do the re-install there is that additional cost. I would try ebay, there are two HP boards listed there. They both are HP Compaq dc5750 motherboard with no IDE ports and with four SATA ports.
With the going rate of BTX, have you considered computing the cost of an ATX case and mobo? I think by the time you find a BTX board, the cost might be simply not worth it. (Just like trying to find a S478 board these days).