Not quite clear on the problem.  It seems to be that you have a new
battery, but you can't start (goes flat very quickly).  Then you can
jump start easily, so there's not a problem turning over the engine (ie
not an unusually heavy drain from the starter motor).  If I've
understood this all right then there can only be 3 causes IMHO.

For test, turn on interior lights.  Does trying to start cause the
lights to dim more than a bit?  If not, either the starter motor has
gone open circuit, or the connecting wires are loose..  Note: the
accessories are de-energised momentarily when you operate the starter,
but the interior lights should remain on (on most cars - is this
different, other owners?).   Is there any click from the starter motor
relay?  If not, it may be that or the wiring to it.

If lights do go dim, either your new battery is faulty (not unheard
of).  Try with another battery.

Or might be an unexpected quiescent drain, which you seemed to suspect.
Best way of verifying/measuring that is to put an analogue ammeter in
series with the negative battery lead (NOT when trying to start or you
destroy it and/or its leads!).  Digital not so good as there will
probably be a pulsing on the line.  Not sure about your model but an
XJ40 is OK with about 50-60 mA, and earlier models take about 20 mA.
May be a bit more when an alarm is fitted.  Do not measure with door
open as you will be measuring interior and puddle lamps etc.  I had a
XJ6 Mk 2 once with this problem.  Turned out to be the boot light switch
not opening properly.  Boot light stayed on when boot was closed (and
was of course invisible).

Let us know how you go.