Your current CPU uses the SOCKET AM2+, and the new processor which you want to upgrade to uses AM3. What's the exact Model number of your MOBO, and which BIOS version does it have?
I think AMD confirmed before that an upgrade path is possible, from Socket AM2+ to AM3. I think AM3 processors work on AM2+ MOBOs, because of the memory controllers on this chip (DDR2/DDR3)...But, AM2+ processors won't work on AM3 boards, since it lacks the DDR3 mem controller.
Though, others can correct me If I'm wrong. Even the PIN config is different, 940 on AM2+ vs 941 on AM3. So I think it might work on your board, but please confirm the exact MODEL number.
There's no Athlon II or Phenom II processors in the compatibility list so none of them would work. 1035 is Phenom II processor that requires AM3 socket, appropriate chipset and a lot of power and none of that is available on that MB.