Sounds like you got an unprogrammed card. It happens. I bought a Lilypad protosnap from Sparkfun. Could not load code into it. Tried every trick I know. Sure appeared to not have a bootloader, no matter what I did it just ran its sketch. SPI pins not broken out either. Chased them several times, they finally sent another with a bootloader. To use the first board without removing the chip, I ended up going to Hobbyking and got an ISP to SMD adapter that you press down on top of the TQFP package to access the SPI pins, and got it bootloaded that way. Adapter cost almost as much as the card.
So, you have some options:
Don't buy from e-bay. I generally don't.
Make your own. I do this a lot. I also make stuff that looks interesting and sell it. Cross Roads Electronics
Buy from a known source. When I do buy, I go this route. Especially ICs. Cuts down on chances of getting counterfeits. And don't need to wait 3-4 weeks for stuff to arrive from China. And a lot of times parts from Mouser/Digikey/Newark are less costly too.
That's the one the IDE uses, so yes.
I program standalone 328P chips and projects as Unos, they work fine with 16 MHz xtal & 22 pf caps.
Even redid my old Duemilanove as an Uno, to keep things consistent.
Did this board have a 16U2 on it? That was programmed ok for USB/Serial?