networking - I can't - install Broadcom STA wireless driver, connect to wifi, connect to Ethernet wired connection

I bought a Dell Vostro 2520 two days back and when I clicked wifi icon to connect to my wifi network, I couldn't see mine or any other wifi networks. So I then realized that I need to install a driver so that I can connect to my Wifi network which is Broadcom STA wireless driver. I tried activating it but then an error came on the screen that said

Sorry, installation of this driver failed. Please have a look at the log file for details: /var/log/jockey.log

So then, I tried connecting to my wired connection. But there are a few problems.

I clicked on IPv4 Settings and set the method to Automatic (DHCP). I could get my IP Address and my Netmask but not my Gateway address and my DNS server.

I tried getting my Gateway address by Terminal but all the answers were blank so I couldn't get my Gateway Address.

Kernel IP routing table

Destination blank Gateway blank Flags Metric Ref Use Iface

I also can't get my DNS server cause I have no internet connection. I tried everything I googled to resolve this problem but nothing seems to work. All I'm getting are errors.

Okay so now the Wired connection shows that it's connected but it's not connected. I did the command @chili555 told me to and here is what it says:

07:00.0 Network controller [0280]: Broadcom Corporation BCM43142 802.11b/g/n [14e4:4365] (rev 01)

09:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RT8111/8168/8411 PCI Express Gigabit Ethernet controller Controller [10ec:8168] (rev 07)

Now that my Wired connection shows that it's working but it's not, I got my Gateway address and my name server. I added them in my wired IPv4 settings. But my internet connection isn't working still. :(

UPDATE:

YAY! It's fixed!! Wired and wireless connections are fixed! Thank you so much! :D