Premiere Elements has never been very good with backwards compatibility. Opening an older project in a newer version of the program almost always leads to problems -- especially with VERY old versions of the program (and yours is ten years old). So definitely do not plan on upgrading and then pulling your current projects into the program. It will only lead to heartache.
That said, frequent crashes can be caused by a number of things. Like the version of Windows you're using and the need to clean and tune it. Or the format of video you're editing. (What model of camcorder is your video coming from? Version 4 really only worked well with video from tape-based miniDV and HDV camcorders.)
Though if you're using a current operating system (64-bit versions of Windows 7, 8 or even 10), upgrading to a more current version of the program will certainly be a benefit, and you'll see much better performance. You'll just need to start from scratch with your projects. You won't be able to open a version 4 project in version 12 or 13 by any means.
There is no guarantee of opening an older version project in a newer version. That has been said already.
However, I have several versions of Premiere Elements on my Windows 7 Professional SP1 64 bit computer. Among the versions are Premiere Elements 4, 11, 12, and 13. I have been able to open Premiere Elements 4 saved closed projects in Premiere Elements 11, 12, and 13.
There is a marked difference in workspaces and other assets of 4 as compared to 11/12/13, and, depending on what is in the project, do not expect that what worked for me in my specific projects will work for you. But, it is not a given that the task cannot be done in a Windows 7 or higher 64 bit system opening 4 project in 11, 12, or 13.
What computer operating system are you currently using. Keep in mind that Premiere Elements 13 does not support Windows XP, Windows Vista, or Mac OSX 10.7.
After weighing all factors, please re-read and consider the version 4 troubleshooting suggestions already described in a prior post in your thread and explore them before making your decision of what next.
Any questions, please do not hesitate to ask after you have concluded the discussion in progress.
If you choose to follow through with ATR's line, you should DEFINITELY keep a good, safe backup copy of your project. Even opening a version 4 project in version 6 has caused numerous problems and bugs for me.
But I suppose it doesn't cost anything to try. But keep a backup copy of your project file just in case...
I would agree that it is best to work from copy of the original Premiere Elements 4 project file if you opt to open the 4 project in a later version (whatever it is). With a very rare exception involving version 10, if you create a project in an earlier version and open/edit it in a later version, you cannot go back and edit the later version edited project in the earlier project.
But again, I would encourage you to first troubleshoot version 4 first before taking off for another version of Premiere Elements.
Add On...There is no Premiere Elements 6. The versions go 4, 7, 8, 9, 10, 11, 12, and 13.