What type of a processor do you have for your computer? If the "1.3 Ghz" is processor clock speed, I am not sure if I would invest in that computer. Is that processor classed as single core, dual core or other? But assuming that I have misunderstood the "1.3 Ghz" and how it relates to your processor....
1. Upgrade the installed RAM to from 3 GB to 8 GB if the motherboard supports that. With Premiere Elements 10 on Windows 7 64 bit, you have a 64 bit application that can take advantage of the 64 bit system resources.
2. How much free hard drive space do you have of the "800 GB" HDD? You should consider a supplemental drive probably at least 1 TB (internal or external, with NTFS formating).
3. Is your video card drive up to date according to the web site of the manufacturer of the video card?
4. What are the pixel dimensions of those 70 photos that went into the slideshow?
Your camcorder shoots in a number of modes. If you are shooting in 1080p, your computer may be a bit underpowered to handle the footage. Particularly with version 10. Version 11 of Premiere Elements is optimized for 1080p and does a much better job of working with it. How well the program will handle any footage depends on how well you matched your project settings to your video specs.
With version 10, you also must set up your project manually --- something that is handled automatically in version 11.
When you started your Premiere Elements project, which settings did you select? You can see but not change your project settings under the Edit menu. What settings are listed there? If you've properly set up your project, you will see NO red lines about your clips when you add them to your timeline in Timeline mode. Is that the case with your project?
Have you resized all of your photos to no larger than 2000x1500 pixels in size (for a DVD, your photos should be no larger than 1000x750 pixels in size) before you brought them into your project? Nothing slows the program like photos taken directly from a camera, which may be many times the size of a 1920x1080 video frame.
You also should render your timeline (by pressing Enter) whenever you see red lines above your clips in Timeline mode. Have you been doing this?
So there are a number of things going on -- most of which are related to how you set up your Premiere Elements project and how you prepared your photos before you brought them into your project.
We can help you, but we need to know what your video specs are. For that Sony HDR-CS580, you need tell us whether you're shooting in PS mode (1920x1080p) or FX mode (1920x1080i). Then we can recommend how to properly set up your project.
It might also help to check out my free 8 part Basic Training tutorials "Intro to Premiere Elements". Part 1 deals with how to properly set up a project.
And, yes, if you're going to run a 64-bit operating system, you really should have 4-8 gigs of RAM minimum.
I have both Premiere Elements 10 and 11 on Windows 7 64 bit and Windows 8 64 bit and have not observed any optimized effects of one over the other, for 1080p or other footage. If your computer is underpowered for the HD video editing that you require, then I do not believe a change of program from 10 to 11 will remedy that.
And, although version 11 takes over setting up the project preset for the project, sometimes it does it OK and sometimes it does not and you have to set it yourself.
The way you or some automated process set up your project can definitely influence the performance of the project, but that assumes an optimized computer with adequate resources to start with.
But there are things that you can do to give yourself an edge in the area of Premiere Elements 10 and computer resources besides the obvious increase of installed RAM and free hard drive space.
a. Check for pile ups of preview files and conformed audio (cfa and pek sets) in the Adobe Folder; and for pile ups of conformed video (.mcdb files) accessed from Edit Menu/Preferences/Media.
b. Use a computer optimization program such as ccleaner with its regular and registry cleaning opportunities.
c. Avoid multitasking.
Just some thoughts for now until we get further input on your computer environment and Premiere Elements workflow.
Perhaps I can get a better perspective on all this if you indicate which type of situation this represents
a. worked before but not now
b. never worked at all
(this in regard to the slowness of your Premiere Elements 10 on Windows 7 64 bit)