Hi:
Below is the link to the product specs for your notebook.
HP Pavilion g6-2235us Notebook PC Product Specifications | HP® Customer Support
It does not come with built in Bluetooth networking hardware, which is why you can't connect your speaker to your PC via Bluetooth.
You can install a USB Bluetooth adapter, or replace the internal wireless card with this model which you should be able to find on eBay. Search by the HP part number, not the model of the wifi card.
Broadcom BCM943228HMB 802.11abgn 2×2 Wi-Fi Adapter, Broadcom Bluetooth 4.0 Adapter HP part # 730668-001.
This card will also give you dual band wifi.
730668-001 | eBay
Below is the link to the service manual, where you can find the wifi card removal and replacement procedure...
h10032.www1.hp.com/ctg/Manual/c03593126.pdf