Can USB devices overload your computer by drawing too much power?

[RichWPX]

So I recently had this portable battery for phones hooked up to my HP Pavillion:

http://www.amazon.com/gp/product/B00UBDI7EC/ref=ox_sc_sfl_title_1?ie=UTF8&psc=1&smid=A142BGUZC6UH73

Ran great no issues... that is until I hooked up this other battery at the same time.

http://www.amazon.com/Aukey-10000mAh-Portable-External-Supported/dp/B011U0AY22/ref=cm_cr_pr_product_top?ie=UTF8

I also had an externally powered HDD, a USB only pocket drive, a mouse, and a keyboard that both light up hooked up. When I plugged in the black battery to my hub the lights on my other devices went out... that should have been a clue. But instead I plugged it in to the main port and it seemed to be working. I left and came back 30 mins later to find my laptop powered down. If I try to turn it on, an LED flashes three times and that's it. It seems completely broken, any ideas?

 

[CountMike]

It sure can, specially those battery chargers, they draw too much power. Laptops even more than desktop computers.
The USB 1.x and 2.0 specifications provide a 5 V supply on a single wire to power connected USB devices.
A unit load is defined as 100 mA in USB 2.0, and 150 mA in USB 3.0. A device may draw a maximum of 5 unit loads (500 mA) from a port in USB 2.0; 6 (900 mA) in USB 3.0.