Can anyone help me out!!

Hi all I have a 2004 rx8 and it's my pride and joy! But after being sat for 5 days she won't start! The starter motor is 4 months old and is the upgraded version, as advised by Mazda. When you try to start the car the starter motor sounds different high pitched almost like a vacuum hoover! It's not clicking or knocking. And she just won't start! But when I was onroute to the dealer (expensive) I was being towed and I thought I'd try to bump start her, and she coughed into life! I run the engine for 45 minutes and shut off correctly then 5 mins later I tried to start her again and she started perfectly! WTF!!!! Please help! I thought this could be the ring gear but now I don't know!!!
Thanks all!

 

more info: Was it cranking? You may have experienced a flood event

 

It was just a really high pitched sound as thou it wasn't engaging!

 

I also tried the deflood routine three times!

 

Well.............back before it wouldn't start........was it shut off cold?
It's also possible after sitting for 5 days(if real cold) that maybe you have a weak battery and jump starting it allowed the alternator to re-charge the battery enough?
Think I'd go have your battery tested for free at Autozone or somewhere or be prepared for a possible repeat.

When you did the deflood three times, which procedure did you use, and did you ever try it with a new battery/jumping?