Control Panel > System ... What do you see at the very bottom in the section entitled "Windows Activation"?
Places online that sell just a product key are usually a scam; the key may work for 3 or 4 months but they are selling the same key to many people so Microsoft eventually shuts it down and then all the people with that key are no longer legal.
Your best bet is to buy an OEM DVD & license. Microsoft doesn't offer free support to OEM versions because the manufacturer or system builder is supposed to provide the support, plus the OS can never be transferred to another computer, but these limitations also make the license cheaper. Be sure to get the bit-size you need (32 or 64-bit) because they do not come with both disks like the full version.
The place I usually check is
Newegg ; they have Home Premium for US$100