You will first have to upgrade your graphics card IF your video conversion software uses GPU. Getting a 4GB graphics card will surely help. The Graphics card puts away specific memory for video or playing games so this is the first chice.
Your RAM comes next. With 8 GB of RAM, heavy programs will get faster since there is more space to write on. Also make sure you dual channel them (i.e. having 2 X 4GB or 2 X 8 GB) so that your video conversion programs can read and write to the memory sticks at the same time. Since you have 3 GB memory, I'm sure it isn't dual-channeled.
Also upgrading your hard drive to an SSD wil make the video conversion fast as it will make the read/write from the hard disk faster and so there will be a guaranteed rise in speed. SSDs perform very well but are not very cheap.
Next, your CPU comes along. It doesn't play an important part but may act as a bottleneck if you have a very low performing cpu like the dual core or pentium and an intel i5 or i7 will do the job nicely.
An important aspect you have forgotten is the motherboard. If it is an outdated one, it will have a slow memory transfer. If the motherboard is outdated, instead of upgrading the motherboard, I suggest that you get a new computer that can handle these tasks.
Overall, if you want a surge of speed, I suggest you get an SSD if you don't have one already but in the long-run, getting a new computer is more advisable, since upgrading specific parts in your computer will usually not be compatible with the older components.