1. Broadcom 802.11n Network Adapter Driver
2. Broadcom 802.11ac Network Adapter Windows 10

Hi,
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From the issue description, wifi will not connect automatically to home wireless network. I will be glad to assist you on this issue.
Method 1
I would suggest you to reset the network adaptor settings. Then follow the steps below

To reset the TCP/IP stack go to this article and either click on 'Fix it for me' or follow the instructions to fix it yourself:

Method 2
Disable the IP Helper service:
a. Hold the Windows key and type R, enter 'services.msc' (without the quotes) and press Enter
b. Scroll down to the IP Helper service, right click on it and select Properties
c. In the dropdown box that says 'Automatic' or 'Manual', set it to Disabled and then click on 'Apply'
d. Then click on 'Stop' to stop the service from running in the current session
e. Click OK to exit the dialog
Method 3
Disable the DHCP Broadcast Flag: Link:
http://support.microsoft.com/default.aspx/kb/928233

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Important: This section, method, or task contains steps that tell you how to modify the registry. However, serious problems might occur if you modify the registry incorrectly. Therefore, make sure that you follow these steps carefully. For added protection, back up the registry before you modify it. Then, you can restore the registry if a problem occurs. For more information about how to back up and restore the registry, click the following article number to view the article in the Microsoft Knowledge Base:
http://support.microsoft.com/kb/322756

(How to back up and restore the registry in Windows)
Windows Vista cannot obtain an IP address from certain routers or from certain non-Microsoft DHCP servers
To resolve this issue, disable the DHCP BROADCAST flag in Windows Vista. To do this, follow these steps:

a. Click Start, type regedit in the Start Search box, and then click regedit in the Programs list.
If you are prompted for an administrator password or for confirmation, type your password, or click Continue.
b. Locate and then click the following registry subkey:
HKEY_LOCAL_MACHINESYSTEMCurrentControlSetServicesTcpipParametersInterfaces{GUID}
c. In this registry path, click the (GUID) subkey that corresponds to the network adapter that is connected to the network.
d. On the Edit menu, point to New, and then click DWORD (32-bit) Value.
e. In the New Value #1 box, type DhcpConnEnableBcastFlagToggle, and then press ENTER.
f. Right-click DhcpConnEnableBcastFlagToggle, and then click Modify.
g. In the Value data box, type 1, and then click OK.
h. Close Registry Editor.

Broadcom 802.11n Network Adapter Driver

By setting this registry key to 1, Windows Vista will first try to obtain an IP address by using the BROADCAST flag in DHCP Discover packets. If that fails, it will try to obtain an IP address without using the BROADCAST flag in DHCP Discover packets.

I hope that this information helps. Please get back to us if you have any more questions about this issue.

Broadcom 802.11ac Network Adapter Windows 10

Hope this helps!. Let us know if you face any difficulty or have any other question on Windows.