The inability to connect to Origin is usually a blockage of data somewhere along the route of your Internet connection. Here is a short list of some of the things that can stop you from connecting:

Firewalls

Software firewalls on systems and hardware firewalls on routers will prevent your computer from connecting to our server. Check with your Firewall's manufacturer to learn how to adjust your Firewall settings and allow Origin to connect.

Server outages

Occasionally servers will experience an outage. Typically an outage can last from 24 to 48 hours. Check the official website for the game you are trying to access, or the official game forums, for any information on server outages.

Internet security software

Internet security software will block or filter information that may be vital for the software to run. check your Internet security software and adjust its settings to allow Origin to access to internet

Scheduled service maintenance

During a scheduled maintenance you will not be able to connect to our servers. Check your game's official site or information on server outages.

If you continue on experiencing connection issues, it is possible that some of the following ports to connect to our servers are closed or blocked from your connection. The blockage can either come from your connection, or your ISP.

In order for Origin to connect to our servers and function properly, you will need to verify that the following ports are open:

TCP ports:

80
443
9960-9969
1024-1124
18000
18120
18060
27900
28910
29900

UDP ports:

1024-1124
18000
29900

Losing Connection to EA Servers

If you are having troubles connecting, or losing connection to our EA servers, please read the information below.

First: Are you using a Microsoft/Sony suggested router? The Microsoft and Sony support pages have a wealth of information on how to properly set up your console in your home network including lists of recommended router types.

Xbox360: http://support.xbox.com/en-US/xbox-360/settings-and-initial-setup/console-setup
PlayStation3: http://us.playstation.com/csimg/global/PS3_CBLrouter_1_0.pdf

If you’re using a wireless router connection and experiencing connectivity issues, try plugging your console directly into the router.

If you’re directly connected to your router and still experiencing connectivity issues the problem is more than likely, your NAT type. The easiest and most simple way around these issues is to enable UPnP or Universal Plug-n-Play.

First, you need to access your router’s config page to see if it supports UPnP. Router config pages can usually be found on any literature that came with the device, or even the manufacturer’s website.
Usually this is a separate portion of the config page that allows the user to check or uncheck a UPnP box (enable or disable). Once you find this box, enable UPnP and back out.
Save your config page changes and reboot your console. Performing a Network test now should reveal that you NAT is open the optimal Online gaming condition
Play through a full game to see if the problem persists

The steps for PlayStation 3 are exactly the same except you would change the specific port numbers to-