Q: Why is my Mac computer taking so long to connect to a network

try deleting your network, and recreating using connection doctor

How long does it take?

First contact your ISP.  You need to confirm that the issue is not on their end.

Change your router channel.  Sometimes this is all you will have to do.

Power cycling the router.  Read the router's user manual or contact their tech support for instructions.

System Preferences/Internet & Network/Network

Unlock the padlock

Locations:  Automatic

Highlight Airport

Click the Assist Me button

In the popup window click the Diagnostic button.

System Preferences/Network- Unlock padlock.  Highlight Airport.  Network Name-select your name.  Click on the Advanced button.  Airport/Preferred Networks-delete all that is not your network.

Place a check mark next to "Remember networks this computer has joined."  Click the OK button and lock the padlock.  Restart your computer.

http://support.apple.com/kb/TS1920 Mac OS: How to release and renew a DHCP lease

No internet connection (wireless)

Check to see if an extra entry is present in the DNS Tab for your wireless connection (System Preferences/Network/Airport/Advanced/DNS).

Delete all extra entries that you find.

Place a check mark next to "Remember networks this computer has joined."

Other resources to check into:

Troubleshooting Wi-Fi issues in OS X Lion and Mac OS X v10.6

Configuring 802.1X in Mac OS X Lion and Later

Non-responsive DNS server or invalid DNS configuration can cause long delay before webpages load

Netspot

How to diagnose and resolve Wi-Fi slow-downs

Pv6 troubleshooting

Mac OS X 10.6 Help:  Solving problems with connecting to the Internet

What Affects Wireless Internet?

Solutions for connecting to the Internet, setting up a small network, and troubleshooting

If using one of Apple's Airport routers, read its user manual or post in the AirPort forum area. 
AirPort + Time Capsule Support is where you can find the user manual.

I have been told that it is a Safari thing.

I do not use Safari.  Post in the Safari forums to see if the users there are experiencing the same issue as yourself.

/Library/Preferences - trash the com.apple.systempreferences.plist file then do the following......

Disconnect all peripherals from your computer.

Boot from your install disc & run Repair Disk from the utility menu. To use the Install Mac OS X disc, insert the disc, and restart your computer while holding down the C key as it starts up.

Select your language.

Once on the desktop, select Utility in the menu bar.

Select Disk Utility.

Select the disk or volume in the list of disks and volumes, and then click First Aid.

Click Repair Disk.

Restart your computer when done.

Repair permissions after you reach the desktop-http://support.apple.com/kb/HT2963, empty the trash and restart your computer.  A new plist file will be recreated after you use System Preference again.  Post back to let me know if the padlock remains locked.

Also when I lock the lock it will not let me apply.

It's not suppose to!  That's the purpose of the padlock once it's locked.