You are not alone brother, same here (excluding the fake stuff - i don't know where your school got that from )
I'm pretty sure your school doesn't want any upgrade that costs a butt load of money (because there are 20 PCs.)
Firstly, you can suggest them to increase the RAM. I think that's the LGA 775 socket with DDR2 RAM. So get some RAM. It won't be that of a cost. 20 DDR2 2GB stickswould cost about 70$, and if its in bulk, you can also get the price reduced.
As for the processor, I am not that familiar with the 775 socket so all I can say is find some decent processor that fits you bill and is better than your 2160 and use that.
Now all this is worst case scenario. If the school is willing to get brand new computers, either get assembled ones which is easier. or you can setup this one .
PCPartPicker part list: http://pcpartpicker.com/list/p9JZJV
Price breakdown by merchant: http://pcpartpicker.com/list/p9JZJV/by_merchant/
CPU: AMD 5350 2.05Ghz Quad-Core Processor ($37.99 @ Newegg)
Motherboard: ASRock AM1B-M Micro ATX AM1 Motherboard ($29.99 @ SuperBiiz)
Memory: Crucial 2GB (1 x 2GB) DDR3-1333 Memory ($11.00 @ Amazon)
Storage: Western Digital Caviar Blue 320GB 3.5" 7200RPM Internal Hard Drive (Purchased For $0.00)(Use your existing HDD)
Case: Xion XON-310_BK MicroATX Mid Tower Case (Purchased For $0.00) (The existing case is fine.)
Power Supply: EVGA 430W 80+ Certified ATX Power Supply ($24.99 @ Newegg)
Total: $103.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-09-14 02:58 EDT-0400
This thing can even 'play' GTA IV
So that's 100x20=2000$. This would be such a huge upgrade for your school. Hope your principal agrees with your opinion
All this is the base idea. Feel free to tinker with it.u
[Whoa! Had fun writing this post ]