Welcome to the forum.
When you click on New Project, a New Project will Open. Note: it takes a moment, but there is a little bar with diagonal stripes, that runs below New Project, so just be patient - it takes a moment, and you should then get a blank Project Timeline. This will be an AVCHD Project, by default, but once Open, you can alter that, as needed, by just going to File>New, to set the Name, Location and then the full specs of that New Project. As PrE 11 & 12 will automatically alter the Project Settings per the first Video Clip added (normally, with most Video media), the default will change to match. However, I like to manually set that, as I need, so use the File>New for those specifications, per this screen-cap:
Note: that is for PrE11, but is essentially the same for PrE12.
What computer operating system are you running your Premiere Elements 12 on?
I have been battling Premiere Elements 12 on Windows 8 and 8.1 64 bit. Major issues
a. Minute or more to open File Menu/New/Project and over 1 minute for the program to close after I hit the close button. The performance of the program is otherwise acceptable.
The irony is that I have Premiere Elements 11 on the same computer that has none of these issues.
But, keeping in mind that problems with the same symptoms can (often do) have different causes, I will ask you the following
a. What computer operating system and what are the computer resources?
b. Is your video card driver up to date according to the manufacturer of the video card?
c. Do you have the latest version of QuickTime installed on your computer? Are you running Premiere Elements 12 as Run as Administrator or from a User Account with Administrative Privileges?
d. Have you shutdown Services and StartUp programs running in the background?
e. Have you looked at the problem with and without firewalls and antivirus disabled?
f. Are you installing from purchased download files from Adobe or from a purchased installation disc?
g. Do you have other versions of Premiere Elements on this same computer that are starting and running and closing without issue?
h. How long are you waiting after you click New Project? How do you shutdown the program when you find yourself in this situation? Where are you selecting "new project"...in the Welcome Screen or in the opened program using File Menu/New/Project?
Let us start here and then gauge the situation and remedies. It should be noted that, at the present time, I am not have any issues with Premiere Elements 12 on Windows 7 64 bit, only Windows 8 or 8.1 64 bit.
Out of curiosity. What computer operating system are you running your Premiere Elements 12?
And, just how long did it take for the new project dialog to show up after you went the route File Menu/New/Project?
Right now I suspect that the user is at the Welcome Screen trying to get in.
PrE 12 WILL go onto Win7-64, but I have not had time to install it onto that laptop yet. Probably will not be done, before about mid-Nov, when I have more than a day at home.
Right now, I am running PrE 11 on XP-Pro 32-bit, so the "load time" is probably longer than it will be with PrE 12 64-bit on Win7-64. Right now, loading is rather slow for me.
As for where the OP is, you could well be correct.
I am still waiting for your details, but, if you are hung up at the Welcome Screen, then, if you are on Windows 7 or 8 64 bit, go
Local Disc C
Premiere Elements 12
and in the Premiere Elements 12 browse for "Adobe Premiere Elements.exe" and double click it an attempt to open to Premiere Elements 12 workspace.
Do not select "Adobe Premiere Elements 12.exe" since that is the one associated with your current desktop icon. It will take you on the Welcome Screen route...where I suspect you are now.
If necessary, we can create a shortcut to the Adobe Premiere Elements.exe file for use on the desktop.
But, your details will hold the answers.
We will watch for your follow up.