I have had my iphone less than a week- i did not expect it to have problems so soon. .... i have iphone 2g my battery ran out now it wont recharge or turn back on? .... but it doesn't turn on, it only vibrates when I try to charge it. .... and showing apple but not going on.i keep start my iphone till bettery dead. ...

best learn the principles of your tablet first
first when a battery is less than 10% it takes up to 5 hours to recharge not 5 minutes
next many tablets do not recharge when in operation so you have to shut down to allow the recharge to work
because the battery was dead flat , of course it will reset as that is the same as removing or installing a new battery

Not enough g's

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take it back for a warranty exchange unit

I went to reset my iphone to restore it to factory settings and it never came back on. It's been a week or two and it ran out of battery power a couple of times, but it just shows the apple logo and a spinning circle over it.

I have a feeling that when you ran the battery down it is now struggling to get and hold a charge.
If you have a friend with a similar battery perhaps try that, or go to a mobile store and ask them to try a new battery for you.

It really could be the batteries. You may want to buy a very good pair of high power Duracell or Energisers first just to make sure that the problem is not with the camera.

I bought my mother this HDC-1061E camera and it was fine for not very long until it seemed the batteries that came in the camera box ran out. A short time. And I offerred a new pair of batteries I found lying around, they were cheap batteries I would use for something not requiring much power. And they brought the camera on but it went off within a second or two each time.

Though then I recalled an 8.2 mexapixel camera I bought for myself last year made by Kodak, and I found that some cheap batteries would not even turn that camera on. And expensive duracells didn't actually last long at all.

What's the solution? Buy a couple of 4 packs of NiMh (2700, no less) batteries (UniRoss is a good buy for this, around £9.99 a 4 pack in Amazon), and a recharger separately. If you're thinking about the environment you should think about a solar recharger though that will recharge a good amount slower than recharging from the mains (there are some more expensive units, if you look around, that offer solar and mains recharging).

I suggest two 4 packs so you have the batteries you are using, another set to exchange for a long day out (maybe not so long in fact, these cameras eat batteries so quickly), a further pair of emergency batteries, and then a pair kept always at hand at home if you need to load fresh batteries at any time. Recharge as soon as used.
A cheapish mains recharger won't cost more or much more than £13 to £20 and may esaily be a few pounds less. Solar rechargers are available in this bracket too, usually a little more expensive than mains ones. If you buy the battery I have specified this should work fine.

This is because your battery is so flat it doesnt even have the power to turn off properly,and the program does often get "stuck" when this happens. Remove the battery, recharge the phone and it should be ok.

Try using another cable or charger. A damaged charger or cable could cause it not to charge. 
Otherwise, contact apple or apple store for repair.

rechargible batterys need to be charged before used on anything