To alter settings you don't need to have the it in the holder.
But it obviously has to be in the holder to work.
If you check out the front wheel there should be a magnet attached to one (or 2) of the spokes.
There should be a sensor on one of the fork legs that the magnet has to go past.
The sensor detects the passing magnet and sends a signal to the computer. There should be a thin wire from the sensor to the holder. (Unless it's a wireless one?)
Fit the computer and spin the wheel to make it work.
If it doesn't work then the sensor might be near enough too the magnet.
Another test:- If you look on the back of the computer there will be 2 bare metal contacts.
Get a piece of metal wire (paper clip) and short the 2 contacts out. Flicking the wire across both contacts should make the computer work if it is working O.K.
You will need to go through a procedure to set the computer up.
Usually:-
Set Km or Miles.
Set wheel circumference.
Set time.
Here is an Echowell instruction sheet that may be similar to yours:-
http://www.echowell.com.tw/images/product/Beta_Set_en.pdf
It mentions pressing the "ALL clear key".
There may be a reset button (small hole?) on the back of the computer or you have to remove the battery and then re-insert to cause a reset.
Hope this helps.