The new graphic card (Asus Radeon HD 6850) I bought, however, is able to fit into the bigger case. I could use the graphic card for my older smaller PC case but the graphic card is too big to fit into it.
I was thinking that maybe I could modify the case so that my motherboard from Aspire AX3950 (maybe its an ITX motherboard) can be used with this new big PC case; like cut it off or something?
Is there any solution other to this? My father would want to buy me a new motherboard for this big PC case but that would need much investment. Please give me ANY KIND of solution to replace the motherboard from AX3950 to this new bigger PC case, either they're "normal" or "stunt" or "abnormal but that could make it work".
Unless the case was btx, the acer board should fit. It should fit inside most atx or micro atx cases. Check craigslist for used cases. Some are as low as $10. Here's one replacement board for socket 1156: Asrock H55M-LE for $64.99 at newegg.com. Your acer board should be micro atx, so getting another used case may be cheaper unless the board has a special connector from the power supply.