Would you buy oats for a dead horse?
I'm guessing no.
Similarly, I wouldn't upgrade that PC if I could help it.
As you see, the old DDR2 RAM is more expensive than current DDR3 RAM. You can't use DDR2 RAM in a Core i7 or i5 or anything similar.
You can buy 16 GB of high quality DDR3 for maybe $100.
You can find out if you are using all of your RAM by looking at Resource Monitor on the memory tab. It looks like you now have 8 GB. No point in getting more if you aren't using all of the 8--even if it were cheap.
Your processor is 5 or 6 year old technology at best. A strong horse.......in its day.
In what way is the PC "slow" and is that a new development? Slow at what?