USB-serial converter based on the FTDI's FT232RL works well also.
Based on writing my own (I want to log directly to disk), I found that the issue is parity. The UT61E (v4.01) stock software insists on even-parity. If your USB converter doesn't support parity, the stock software wont connect to it.
Try opening a regular VT terminal. I am not sure what VT terminal Win10 is packaged with. On Win-XP it is the Hyper Terminal. Set the port to 19200,7,1,N. (Stock software connects using 19200,7,1,E; but here use N for no parity)
If parity is the issue, connecting with 19200,7,1,N, you would see lines of text coming into your terminal software every 0.5 second or so. In that line of text, you should see the reading value itself. For example, if it is 9.876 K Ohms, you should see 9876 in the text. The range and reading type is also represented in the text somewhere as bit codes and are not directly human-readable like the number.
If you do find parity to be the issue, you know your DMM and the PC are talking to each other. For the stock software, will need a different USB converter that supports parity like the FT232RL chipset ones do.