Ummm, read the motherboard manual. Does it say they are SATA1, SATA2, or SATA3? All SATA drives are backward compatible, so a SATA3 drive should work on a SATA1 port although this will effect the performance of the drive since it must run slower than it's designed to.
If this is a new board, it should be SATA2 or SATA3.
You have been very kind. I appreciate it. I haven't opened it up yet, but I have the specs from the website (I copied them because I bought this computer in 2009 and I know that it wouldn't be available forever). All the specs say is "Systemboard with Intel® X58 Chipset." I don't think that the chipset is enough to be able to tell, is it? The specs do say that the hard drive is 1TB SATA and the external ports include two sSATA ports. I will look in the case and see if I can find the motherboard make and model. Thanks again!