Hi Heligone,
It would appear to me that the makers of the board intended it to be used whilst recieving power via the USB port and drawing on the battery as required when doing things like a "AT+creg" type command.
My limited understanding is that you must have both power sources in place and charged/ready to go before trying to do anything such as connect to GPRS etc...
Sounds like you are trying to charge your battery from Solar while relying on it as the only power source? Maybe I'm not reading what you said properly though.
Cheers