WELL WELL, after much hair pulling and troubleshooting and experimenting, I got it to work!!!!!!
I'll let everyone what's going on, because other people using the B75937 USB to FTDI will need to know this. (this is valuable information)
First of all, this little adapter does not come with a DTR pin that the Ardweeny needs, but it does have a small through-hole soldering point for a pin. I pulled out my soldering iron and using a spare row of header pins I had left over from another project, I made myself a DTR pin on my B75937. It took me 5 minutes.
Secondly, there is a mis-print on the board of the B75937, which would explain why it was so cheap. ($2.50 including shipping). The TXD and RXD labels are mistakenly switched. The proper connectivity is TXD -> RXI and RXD -> TXD. Once I had switched the connection, and had the DTR connected, my Ardweeny (which I am very happy with) came to life!
I hope anyone googling problems with their B75937 USB to FTDI serial adapter with CP2102 chip can find this information handy and save themselves some frustrations.