Ranked Mediator :
Okay, that computer has an Intel® 4th generation Core™ i5 Quad Core processor which is good for gaming , however , it has only Integrated Intel® HD Graphics 4600 which is really and truly not good for gaming. If you could get a cheap low end graphics card, then you would have a chance to run low end games like LOL, CS:GO, Minecraft etc.
Well, you could have suggested something. Here, I'll try:
Your computer probably only has one PCI slot. Hope that's not filled with a wireless card. Your power supply is a 400 watt or under (usually 300w). There's only two cards you plug and play without changing other parts. So, leaving your computer exactly as it is, you can get a Unique GTX 950 (not any old 950) or a few 750ti. All of the 950's except the ASUS GTX 950 2G-model, require extra power cables. Some of the overclocked 750ti's require extra power cables. The 750ti's are cheaper, and weaker, but will allow you to game at moderate settings on 1080p or lower panels. The 950 is more powerful, and will let you game with more settings turned higher, but will cost more, and to be honest, it was just announced and I couldn't find any for sale. So considering the state of your free 'office' tower, I'd just grab one of these:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814487114&cm_re=evga_gtx_750_ti_superclocked-_-14-487-114-_-Product
and call it 'JOB DONE' until you get money for a new computer.