Go to Harm and my PPBM5 benchmark database. Notice that there are 860 results shown. Select the "Computer type" Tab and then select "Laptops" go to the bottom of this list and you will find an Intel laptop with a better processor than yours, and it is 854th place in this test. You might be able to set a new low mark with you T 4500 processor. If you are only editing Standard Definition miniDV video it might work. It would be impossible to handle any complex codec's like AVCHD
Oh, and you did not tell us if your OS is 64-bit which is required
That laptop of yours is far too weak for the type of video that you'll be editing. In fact, if a fast PC takes an hour (or a fast laptop takes three to four hours) for a given AVCHD content, your laptop may very well take all of three days (72 hours) to render that same amount of that same video. An analogy to this would be driving a beat-up old jalopy whose transmission is permanently stuck in first gear on a road that's designed to be used by modern high-performance sports sedans.
And in my experience, no dual-core CPU-based PC - not even a desktop - performs as fast in Premiere as even a quad-core CPU-based PC of merely average performance. In fact, my Core i3-2100-based desktop PC, though it was the fastest of all PCs with dual-core CPUs in the PPBM5 results list, is still outperformed by several laptops with quad-core CPUs.
Other bad points: The built-in screen has too low of a resolution to display the Premiere Pro interface properly. Some vital portions of the interface will be cut off, with absolutely no way at all whatsoever to retrieve this cut-off portion. This is because your display has a vertical resolution of only 768 pixels. Premiere Pro requires a minimum vertical display resolution of at least 900 pixels and a horizontal display resolution of at least 1280 pixels just to properly display the UI.
Some ideas for a Laptop Video Editing PC from past discussions
For effective HD video editing, a laptop with the following
-at least the Intel sandy bridge 2720 or 2820 quad processor
-and nvidia graphics preferably the 460m, 485m is a bit much
-1280x900 display with OpenGL 2.0-compatible graphics card
-and 8 or 16 gig ram and Win7 64bit Pro
-and 2 internal 7200 HDDs minimum
You are confusing "rendering" with "encoding". "Rendering" is actually done as part of the editing process. What you said "went fine" is actually called encoding (or transcoding), not rendering.
In either case, there is absolutely nothing that you can do to "fix" the molasses-slow editing performance short of having to purchase an entirely new PC.