I think the mobo are the same through the inspiron 1564 range. So if your mobo is dead, I think you can use that as a replacement. But if you just want to upgrade the cpu, just slot the first gen mobile i5 or i7 in, you don't need a new mobo, the HM55 chipset will work. Just make sure you have the right mobo socket cpu combination (rPGA or BGA).
But I sense that you don't have much experience in handling laptop hardware, and I think what you are about to do will be very challenging for your, so I recommend you not to DIY, unless the mobo is dead and you are out of warranty.
Then you have to get your technician to open it and see if it has mxm gpu or one that is solder on the mobo. If it is mxm, you can get one online. There is an online store specialize in laptop gpu, but I lost its bookmark long ago, try google it.