Trying to run a PIC 16F84 with 2V i came to tihnk if there is any
    possibilities to make a LED to run with only one NiCd that has the output
    valtage of about 1.2 V. Led needs about 1.6 V.
    The system should not have any fancy IC's and it should fit in the size of
    half of an AAA-cell.

An LM3909 "LED Flasher" charges a cap and then discharges it in series with
the battery to drive an LED from a single cell.  While the "normal"
configuration uses a 300uF cap and flashes once a second, presumably
(haven't tried it) a smaller cap would result in a faster rate, perhaps up
to the "apparently continuously on".  Might be awfully dim, though - it's
none too bright in the original config.  About $1 for the chip - the circuit
would fit in your space if you can find SOIC versions.

You might be able to achieve the same sort of thing with a couple
transistors, some IO pins and some intelligent software (sorta like a
standard AC voltage doubler driven by IO pins, which might work too, for
high efficiency LEDs...)

BillW