Is this the TASCAM US-4x4HR USB Audio Interface? When I look at the manual for this baby, it says only WDM and ASIO are supported for Windows. Audacity is shipped with neither. 
I believe cakewalk is free and supports ASIO and you can get a demo of Reaper that also supports ASIO.
If you want to try compiling your own, private, Audacity that does support ASIO, see here: ASIO support in Audacity 2.4.2 - #13 by jademan
I hope this helps. 