bingo... faulty ignition switch and in all likelihood just the electrical portion (very common failure). FWIW, the odometer light does stay on for an extended period after key removal in normal operation as well as I recall.
Part can be had < $10 when bought online through auto haus az . com use
this LINK
Can also sometimes be bought locally at Audi or VW dealers ~ $40 but call ahead to ensure.
Easy DIY R&R Instructions & Part # Link Here ...courtesy of Mike Focke's compilation
In the mean time... be careful of draining your battery b/c ignition system is still active unless you get the "thunk" when removing the key. So, if parking for extended periods, either put on a battery maintainer or disconnect (-) battery cable (remember to not lock the trunk too
) Keep your 4digit radio code handy b/c each time you disconnect battery you will need to re-enter it since your car is pre-'03 when Porsche switched over to the MOST fiber-optic set up.
Good luck