Replaced battery on 04 CBR1000, riding for 30 minutes stopped in store and bike would not start (not holding charge) jumped started, while idle noticed MIL on and bike shut down/stopped. Towed bike home, jumped started the next day engine sounds rough and noticed temp going up and HESD flashing

Sounds like the battery is not holding a charge, if you connect a volt meter just after charging you will get a good reading, each cell of a battery is 2.2 volts so you should have a reading of 13 volts. Battery may have a faulty cell, which will drag the other cells down, is the electolite covering the plates in all the cells, this will affect the battery's ability to hold a charge. My Suzuki did this earlier on this year, nearly bought a new battery, checked and topped up the electolite first and its been fine since

Check if the charging system works ok.
At idle with lights off, you should see 13.5-14.5V on battery's terminals and 0.5V less with high beams on, at idle speed as well as at 4000rpm.
Use a fresh good verified battery to take the readings.

bike will not start or stay running on a full charge battery/bought brand new battery, still same promblem,jump bike off,will crank ,ride bike for 30 min. park bike, leave bike...

This usually indicates there is not enough power to turn the starter over, so the solenoid just clicks. It sounds like you need the battery to be charged. If this is occuring even after 20 to 30 minutes of riding, either the charging system is not working or the battery is bad (motorcycle batteries typically don't last for more than 3 years, less if they are not kept charged during the non-riding months).

Yes the brakes will work if the bike does so you can take a breath of relief because there is no brake booster it is just hydraulic pressure from the hand and foot switch. What i think may be happening with this bike is a faulty regulator rectifier. This will cause the battery to die with the key off AND it will also cause the battery not to charge correctly when the bike is running. It may hold a charge but will not charge further. What this unit will do is keep the voltage consistent from the alternator charge.

Try charging your battery fully .idle running will take too long to charge the battery .Leaving your bike ticking over will not harm it oproviding it is not getting too hot through no air passing over the finning on the engine .

the regulater is located between tha battery and the gas tank .There are (3) white and(2)red wires .See if they are showing signs of damage from heat more than likley they are because when you "boost" or jump these bikes you burn a very weak diode witch regulates the charging time from the stator i would check ebay for the best price on a new regulater rectifier you may need one.I had the same problem with my 2000 model r6.good luck bro!

yes it could cause this
fully charge battery and try again

Check the alternator and battery clemmas/wires coming from alternator. It looks like no charge from it coming to battery. If it is second battery already this is the sign. You can do it free of charge at autozone store. But any way as a temporary solution you can buy battery charger ($25 walmart) and charge the battery back if battery is damaged you will see it right away (it wont be charging). After you charge battery back start the engine run it for 30 minutes (if Alternator OK it is enough to charge battery back), stop and start again. If no start alternator is a problem.
Good Luck

The alternator is not affected by not being used for awhile. The battery is affected. I would bump start the bike then take it on a good long ride to allow the alternator a chance to recharge the battery. Alternate to the ride would be putting a 1 or 2 amp trickle charger on the battery for 3 hours or so. If the battery does not want to take a charge, consider how old the battery is. If it is 2 years or more I would suggest a new battery. Motorcycle alternators seldom fail.