Did the starter actually fail or did you replace it because of this problem? If the oil light is staying on when you crank, then there is no oil pressure. No oil pressure would NOT stop the car starting, so it sounds like the engine is not actually cranking, since that turns the pump and you get oil pressure.
So... did you change the starter and was it a new one? When you crank it over, does the engine actually turn over (have a look at the crank pulley - what's it doing)?
Next one; When the beast had been sitting around for three weeks, did you charge the battery (was it flat) or was it still charged up and you just attempted to start the car? If you had a battery low voltage it may have been not enough to spin the engine, just to engage the starter on its clutch... that whining high pitched sound).
Alternatively, if the battery went stone-cold dead flat you may now have a problem with the immobilisor (low residual voltage might have caused the code to become corrupted compared to the key. If there's not enough juice, the code can't be properly recycled, so it gets out of synch' with the key chip).
It sounds like your battery is a brand new spunky young buck ... so you need to work out what Scotty is actually doing down there in the engine room. Remove one of the HT leads and stick an old spark plug in it. Earth the electrode against the engine block and (take care not to electrocute yourself) crank the engine, to see whether there's a spark.
This test will be useful to prove that the engine is actually cranking over, rather than just a noise from the starter but nothing actually turning. No spark might suggest the engine isn't actually turning over and all the noise is just the starter.
Next, if you have a voltmeter (or a light bulb holder and a pair of wires attached) remove one of the plugs from an injector and connect up to it. When you crank the engine, the injector (multimeter/bulb) should flash.
If you have no sparks and no injection but the engine IS turning over (you'll have to watch the crank pulley as you crank it over), then the problem is related to the immobilisor or potentially the TDC sensor (a code reader would spot this).
Anyways... probably enough things to try for the time-being. Let us know if you actually have sparks and a flash/signal at the injectors while you crank it over. I fear your immobilisor is out of synch' though, which is a bit fiddly .. you would need someone to re-synch the key with the ECU... not a big job (20 mins if you have the kit) but you have the hassle of getting the car to the kit. But don't worry for now.. check the other stuff first.
Ralf S.