2003 e270 cdi wont hold charge

Hello folks, ive recently taken a trip out to europe and have been driving my brothers car. In the past day and a half on the nav display there was a warning sign that stated for me to turn on the car or eveything would shut off in 3 mins(however car was on at the time).

Once i parked the car it wouldnt start but had enough battery to operate the doors windows and radio. I jumped the car and it started right away, and let it charge for about half hour. Once i shut the car off however it wouldnt start again.

Does this sound like a battery or alternator problem?

By the way the battery read about 10.6 volts while the car was running.

Thanks in advance everyone