If the new driver didn't fix anything try this; open Device Manager and in the View menu select Show hidden devices. Locate your wireless adapter, right-click on it, then select uninstall and click OK.
Close Device Manager and shutdown your laptop. Here's the link for the
Aspire 5552G Service Guide. Go to page 65 of 260 (chapter 3, page 55) where it describes removing the lower case covers and then goes on to show how to remove the WLAN Module (wireless card). Disconnect both antenna cables, remove the card, carefully inspect for dirt or damage, then carefully reseat the card and reconnect both antenna cables. Reassemble the case covers, reinstall the battery pack and start the laptop.
When Windows boots to the desktop it will detect new hardware and attempt to install the driver for the wireless card. The driver installation will probably fail because Windows won't have a suitable driver available. Now reinstall the Broadcom driver you downloaded and test if you can connect.