I agree with Ann here. Upgrading that PC is not economically feasible (that is, the total cost of the upgrades is higher than what that entire PC is currently worth) because it requires three or more hardware upgrades just to get its performance up to par. It definitely needs a lot more RAM, a new GPU and one additional SSD in order to achieve that (since the H77 chipset runs only two of its six SATA ports at full SATA III speed while the other four ports only run at SATA II speed). And in addition to what Ann stated about the NVS 300, that GPU would not have been supported at all in Premiere Pro CC 2015.3 or later even if it had a ton of memory because it used the obsolete Tesla architecture, and it is basically a rebadged GeForce 210 GPU that's almost completely useless nowadays for anything. And the additional SSD is required because no 1TB HDD of the same age as that PC could achieve even 140 MB/s (and most couldn't achieve even 130 MB/s) in sequential transfers. Plus, Intel is now out of the motherboard business completely except for a few server boards, so that motherboard is now essentially EOL (no further support).
EDIT: I just re-read the list, and found that the system had 16GB of RAM, not just 4GB. Although 16GB will run Premiere, 32GB is better.