Welcome to the forum.
Unfortunately, you have posted to the Tips & Tricks sub-forum, which is basically a repository for articles on how to do things in Premiere. Few subscribers ever stop by here. I am Moving your post to the main forum, where you will get many more "eyes," and reponses.
First, for the crashes and hangs, I would take a look at this FAQ Entry. It starts with a general checklist on getting PrE running best, then goes into some OS/system tune-up, and ends with a bunch of links on troubleshooting: http://forums.adobe.com/thread/792580?tstart=0
With MTS files, I need to ask if these are AVCHD? If so, then you will want your Project to be set up for AVCHD and not HDV (a different HD format entirely). It might also be useful to know what the make and model of the video camera used to record the MTS files is, as some present specific challenges.
Is all of your Audio from those MTS files, or do you perhaps have other Audio Source files, like MP3's?
Your CPU is going to be weak, for working with AVCHD (or any H.264 CODEC material), but you should only see that in playback, and usually by a lack of smoothness. The 4GB RAM is not a lot, but with a 32-bit OS, is the best that you can do.
The 150GB of free-space on your HDD should be adequate.
I have not read of a failure to Multiplex, but if your Source Material does not match your Project Settings, that could be a result.
I am sure that others will have more questions and suggestions.
Thanks so much - the originals were MTS / AVCHD files originally from a panasonic lumix camera. We have added a couple of audio files, which are MP3 and other formats. Is it possible that simply the audio files are what is preventing the export?
I will review that FAQ and make sure there aren't some quick fixes in our computer that can help.
>audio files, which are MP3 and other formats
It is not usual, but mp3 audio HAS been known to cause problems... convert to WAV and try again