how to determine motherboard body type?

I need pc parts . the question that comes to mind is. i am working with very little money, and i have been to several websites that offer barebone kits and/or parts, but i only need a new tower case, the motherboard, and the CPU. perferably a motherboard that will sync in size for the cpu from a MPC61PM-GM motherboard so i can just reuse the old one i have. (although im not really 100% the cpu is intact /shrug)

So my problem is working backwards.. in finding a motherboard just like if not just a replacment MPC61PM-GM.. and then a case that it would fit in.

my problem is, i do not know what motherboards would fit the cpu form that M-B, and even if i did, i dont know what tower cases would be compatible for that board. i know motherboards come in various shapes and directional designs.. and so matching a case to a motherboard seems kinda daunting for me since i have to do it backwards .. finding a case for a motherboard not a motherboard for a case.

Does anyone have any idea how i could use the CPU for my old MP board in a new MB but also put it in a new case? people keep telling me to "look online" but there are no guides on the pc websites that would suggest a method of how to match a replacment for the current motherboard, or case.

the parts i have to re-use are

RAM,

HDDs,

various fans if nessisary,

a PCIE Gcard,

115-230 power supply

cords etc.

what should i do (im just scraping by on finances)

a little help please i dont know what im doing.