Me, too.
On Android whatever, I could find the IMEI by going thru the menus to find it. Then, prompted by a message from BOAC, I updated to Android whatever plus summat. (2.2 firmware).
Now, I can't find the IMEI and have downloaded the same app as BOAC.
Keyboard comes up for the obvious needs, such as texting.
Otherwise, one has to go to Phone, and Keypad.
That might be the answer, as to enter *, etc on my old phone, I had to have the phone keypad working.
In fact, thinking about it , that must be the answer. Press phone, press keypad, leave keypad highlighted, (rather than, say, call log) and come out. The next time you press phone, it will go direct to keypad.