i have a 04 cbr600RR w/ 3,500mi

so i was pretty sure i had a "infamous" rectifier/regulator problem. the battery will die if i try to start it when the bike is hot. i.e. getting gas. bike is real hot , shut it off to get gas and go to start back up and it dies. or going into a store for a few mins. i thought it was the regultor. i ordered one, put it on this morning. bike started fine checked voltage at idle and reving. all good. drove it around town for 10 mins and while i was cruising i go to shift and the battery dies as i pull in the clutch. so i coasted to a stop and i couldnt start it. battery just died. im going nuts with this thing
i get it back home in a pick up truck. the battery reads 12.4 volts but wont start. it cranks once and it just clicks and dies.
so i have replaced the regulator, i had the bike on a battery tender the past few days so it was fully charged, and since the battery is reading 12v i dunno if its the battery or something else like a fuse or something.
i would appreciate any help! its driving me crazy and its a huge pain in the ass.
thanks!

Will it fire and run if you push start it?

Sounds like it might be the battery. 12v is low for a fully charged battery. Do you have a local garage that can do a load test on it?

Will it fire and run if you push start it?
i havent tried.im sure it will the bike runs fine. its something electrical or in the charging system.

Sounds like it might be the battery. 12v is low for a fully charged battery. Do you have a local garage that can do a load test on it?
thats what i was thinking but the battery is expencive as ****, and i dnt wanna get it till im positive. and if u rev it up to 5 or 6 grand it reads 13.9 or sumthing. i let the bike run for a while after charging the battery when the fan kicks on it goes down to 12v i dunno if maybe its drawing to much power or somthing. i have no clue,. im clueless with this right now

jus sounds liek every 600 from 03-06 ....the charging systems r garbage on these bikes, prone to stators going out and regulators. battery should read 12.5 or better wen jus sitting and startup it'll drop to about 11v, revving it and it going to 13.9 means the regulators fine, jus take the battery to ur dealr an hav them check it, if its fine might b time for a new stator. but usually wen those go out its all at once and the gauges start flickering an it wnt start at all or stay idled. electrical issues suck!!! hope u get it figured out bro.