Which Zorin version should I install on my computer (Dell Inspiron 1545), I'm thinking of installing LITE to have a better performance but I don't know if it will use both processor cores.
Processor: Inter®Core 2 Duo T6400 (2 GHz)
GPU: Intel Corporation Mobile 4 Series
Ram: 4Gb (2 DDR2 Sticks)
Hard Disk: SSD
Given your specs, either Core or Lite should run reasonably well on your computer. You can make a choice based on your preferred Desktop Environment.
Using Lite may give a small boost in performance.
Use Lite, You will get serious problems with Core according to your specs. I have seen notebooks run on Lite Version (Xfce) and you may also enjoy the same experience
It will use all of the Resources
I have a Inspiron 3502 (n4020 upgrades to 8gb/1tb) use Lite Pro 16, even with added ram the lower spec'd duo CPU will be noticable in Core edition.