The MB has H61 chipset, which does support the r7 260X, as long as it has the pcie2.0x16 slot because pcie3.0 is backward compatible.
1) What PSU do you have? Make sure you have the PSU can power up the r7 260X.
http://www.realhardtechx.com/index_archivos/Page362.htm
2) Do you plug in the 6 pin pcie power cable to the r7 260x? because the r7 260X need get the power from the cable.
3) Do you use nvidia gpu before you get the r7 260X? If yes, you need put back the nvidia card to uninstall the driver by Guru3D - Driver Sweeper
http://www.guru3d.com/content_page/guru3d_driver_sweeper.html then switch the GPU.