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 If it is an outdated one, it will have a slow memory transfer. If the motherboard is outdated, instead of upgrading the motherboard, I suggest that you get a new computer that can handle these tasks.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.
Upgrade the motherboard so you can take advantage of the latest processor and related technology. – Moab – 2016-03-19T14:48:51.550
See the update at the end of question. – Woeitg – 2016-03-19T17:25:51.170
Upgrading the CPU or RAM itself has a bottleneck... the mobo, which won't take newer processors or RAM. The only sensible path is in @Moab's comment, mobo first. Though it will make you do more of the upgrade at one time, assuming such as the old mobo is DDR2 not 3 etc, it is the only method that will not make you do things twice. Upgrading the GPU first will hardly help at all if it's sitting on archaic technology. – Tetsujin – 2016-03-20T17:29:11.467
1It also depends on the conversion program: Update first the motherboard for faster memory & bus. Second the GPU, if the conversion program uses it. Third the CPU, if the conversion program doesn't use the GPU. Fourth the hard disk, for reading/writing files faster. But wouldn't it be simpler to buy a new computer? (Maybe that's why the downvote.) – harrymc – 2016-03-21T16:02:21.107
From economical point of view, it is not a god decision to buy a new computer unless necessary. the reading/writing speed is something I didn't consider, tnx. – Woeitg – 2016-03-21T16:04:12.270
If the conversion program doesn't use the GPU, the best improvement will be by changing to a program that does use it, and getting a multi-core GPU. – harrymc – 2016-03-21T16:06:01.923
I still dont understand the reason for down vote. Buying a new computer is a better solution rather than upgrading a specif part. What sort of reasoning is that? – Woeitg – 2016-03-21T17:41:39.157
The reasoning is that the new parts will not be fully efficient because of the old parts. – harrymc – 2016-03-21T19:07:39.043
@harrymc I agree. tnx for suggestion. – Woeitg – 2016-03-21T19:29:02.637