No. The ability to edit AVCHD footage was not a part of version 4. That ability was not added until version 7 -- and not really well developed until version 10. Simply adding codecs to your computer won't make it happen. The program just hasn't got the stuff to handle it!
In fact, even with versions 10 or 11, you may have trouble editing AVCHD video on a Pentium. In my book, I recommend at least a dual-core 2.6 ghz processor with 4 or more gigs of RAM for editing AVCHD.
So I'm sorry, but you may not be equipped to work with this type of video on anything other than Windows Live Moviemaker.
Convert AVCHD to a "maybe" easier to edit codec http://forums.adobe.com/thread/390605 - but no way to be sure that will work for version 4
Also, installing k-lite MAY cause problems
>sometimes it just crashes or freezes randomly
What MAY help is to right click the program icon and select WinXP compatibility mode from the popup option window
True. AVCHD was not supported until Premiere Elements 7. Those with Premiere Elements 4 on Windows typically converted the AVCHD to another format so that they could use Premiere Elements 4 as the video editor, providing they had enough computer resources for the task. Yet, there were some who could use AVCHD with Premiere Elements 4.0, but they were the ones working from a Sony Vaio that offered a special plug-in for the AVCHD support and the same computer resources considerations.
Putting aside the AVCHD.mts.
What has not been mentioned yet is your report of not being able to work with what you describe a QuickTime (mov) footage. What are the properties of this footage...video and audio compressions, frame size, frame rate, progressive or interlaced, etc? Do you have the latest version of QuickTime installed on your computer with Premiere Elements 4? And, is your Premiere Elements 4 set Run As Administrator and/or from a User Account with Administrative Privileges?
Versions of Premiere Elements earlier than 10 are 32 bit applications which run into limitations of the 32 bit operating system. Computer resources and the demands on it from a large sized project may enter into the mix. But, let us clear up the QuickTime (mov) footage situation.