First of all the clock and remote locking are not connected to the radio,
are you sure that no fuses have blown?

When you switch on the radio what do you see? Does it ask for a code, or is
the display blank? If the latter then you probably have lost power to it,
which might also account for the clock not working.

Have you seen the radio out of the car? You would need to confirm the
manufacturer (Clarion, Philips etc) and type number (PUxxxx?)

Some codes are worked out from the serial number, but as yours has none, it
might be another type where you have to look inside at the circuit board and
check the combination of 8 or 10 connection links. This in turn allows
someone with the right software to work out the security code. I managed to
decode a 106 radio from a scrapyard this way. If it is the type where you
have to look at the circuit board, then anyone doing the decoding will have
to see the radio, hence the need to send it away.
The other way is to buy a more standard radio and fit it. You can get the
surround adaptor plastic from many auto radio places, and on Ebay which
would be cheaper. In fact, if you do a search for "306 radio" on Ebay, you
might find one complete with code, cheaper than the cost of getting yours
decoded.

Best of luck,

Brian.