Does the alternator make an unusual purring or whining sound?  A shorted diode
would both reduce alternator output and drain the battery.

Testing:  Disconnect negative battery cable.  Connect 12v test light between
negative post and removed cable clamp.  If there are no shorts the test light
will not light or be dim (load from ECU, clock, radio).  To check for most
shorts, start by removing fuses until light goes out.  (Remove dome light fuse
first so you won't have keep closing the door to see if the test light will go
out).

To check the alternator, disconnect the large battery lead on the back of the
alternator.  If that is the problem, the test light will go out (or go dim).

Let us know if this helps or if we need to do more checking.