Is the Huwai modem connected via WiFi (Airport, 802.11b/g/n), USB or ethernet to the computer?
If by WiFi or USB try connecting by ethernet.
Ethernet tends to need less drivers.
Also many third party USB devices do not support Energy Saver of the Mac, and will baulk if the lid is closed, or Energy Saver turns on.
If you can run the machine off the internet and get issues, then you can probably run the hardware test with the original installer discs to see if hardware is at issue:
https://support.apple.com/kb/HT1509
Though RAM can be at issue, and it still not be detected. If you bought RAM for it, you'll want to make sure it was purchased for that age of MacBook Pro, and not by the spec, and not ValueRAM.
http://www.crucial.com/http://www.datamem.com/ and http://www.macsales.com/ offer RAM by age of Mac.
The Mac is old enough to need a replacement PRAM battery as well.