You can only brighten a video so much. So a lot depends on a lot.
What device did you use to digitize your VHS video and what file format is the digitized video? Most lower end digitizers -- particularly those that connect to your computer via USB jack -- do not create video files that lend themselves well to editing or effects.
You don't say which version of Premiere Elements you're using, so it's hard to give specific advise.
But generally speaking, video from a non-digital source (like VHS) is particularly hard to enhance and brighten. You'll usually end up with a blotchy, purplish video.
For digitized VHS material, I find that the Three-Way Color Corrector (cannot recall when it was added to PrE?) is a powerful tool.
For underexposed, grainy video, I use Neat Video (3rd party plug-in) to be effective. Note: processing time for Rendering and Sharing will take time and a lot of CPU horsepower. It also requires some experimentation to get just right.
After Neat Video Effect has been added, I will use just a bit of Sharpening (do not over do this) is effective.
As Bill points out, video from a old VHS source would be difficult to enhance as it would kick the grains high and the output might start looking more shabby.
What I would do here is that - (after enhancing the clip to whatever extent you can) Import these clips in a bigger project setting and then Scale these clips down and place them in the center to create a picture in picture kind of effect. With the backgroud being the same clip scaled up to fit the entire screen, but may be with Black and white effect applied and with a good amount of blur applied, so that the background movie does not disturb the foregroud clip.
This trick helps solve a couple of things if nicely done.
1) The old VHS footages are usually of smaller dimension and nowadays the playback monitors are usually HD ones - Creating a Picture in Picture (Video in Video) effect helps showing up the VHS footage in a smaller window and it atleast gives a feel that the video quality has improved a bit.
2) Having the same clip, blurred and with some effects, gives a feel that the entire screen is filled with relevant content.
Do try with a small portion of your footage and check if this helps.