Download and install the LR 4.3 update, and run that in trial mode for a few days/weeks (limited to 30 days), to make sure your machine can handle things.
http://www.adobe.com/downloads/updates/
If for some reason the LR 4.3 install doesn’t offer trial mode, then download the LR 4.0 TRY version from the normal purchase URL then download and install the LR 4.3 update:
http://www.adobe.com/lightroom/
If things go ok, then you can return to the above URL and purchase a LR 4 serial number and use that to convert your trial install to a licensed version.