Hi
Found the StorE TV+ specifications on this Toshiba page:
http://www.toshiba-multimedia.com/eu/store-external-hard-drives/tv-plus/
The Store TV+ supports the video formats:: MPEG1 (DAT, MPG), MPEG2 (VOB, MPG, TS/M2TS/TP TRP), MPEG4 (AVI, MP4, MKV), VC-1 (WMV), H.264 (AVI, MKV,MOV, MP4), RM/RMVB (RM/RMVB)
The MKV files are supported by MPEG4 and H.264 video format.
Are the files recorded in this formats?
How about playing other files i.e MPG or AVI?
Furthermore I would recommend checking the connection to the TV.
Here is a user manual which I found on the Toshiba page:
http://www.toshiba-multimedia.com/Global/Manuals/Store/Manuals/STORE_TVplus_User_Manual.pdf
It shows you how to connect the Store TV+ correctly.