You need to get a free third party app called MPEG Streamclip. Available here. http://www.squared5.com/svideo/mpeg-streamclip-mac.html
Once you have MPEG Streamclip, open it, and drag your MPG file into MPEG Streamclip. Then click FILE/EXPORT TO QUICKTIME. Choose Apple Intermediate Codec for the Compression. Click the "Make Movie" button at the bottom right. Give it a name and put it in a place you can find it.
Now in iMovie, click FILE/IMPORT MOVIE and navigate to the Apple Intermediate Codec file that you just saved.
There is a chance that you will need one additional piece of software. If you get any error messages, come back and I will walk you through that part.
click on video, right click and go to encode file for greater compatibility.
You can convert that file to prores or something else.
Not to take awayfrom the Mpegstreamclip suggestion, as that is one of the greatest tools in a videographer's toolbox, and it's free.
I have the same problem with my .mpg files and iMovie not playing sound after importing. However if I look at the quicktime MPEG2 Playback Component a warning is given that this plugin will not work for Lion.
How can I convert these .mpg files now?
Use MPEG Streamclip. MPEG Streamclip will tell you if you need the Apple QuickTime MPEG2 Playback Component. If you do, use the Beta Version of MPEG Streamclip and follow the directions on their website for installing the Apple QuickTime MPEG2 Playback Component.