Well hang on a minute, if you don't crash with bots, say 9 of them, and you can play full games with them, your crashing online is more likely than not nothing to do with your PC.
I'm not sure if any internet, ISP or related hardware (Router, Modems etc) can play any part in you crashing out of the game, but I'd suggest at least that you try to delete/uninstall the game and redownload/reinstall it, it sounds more of a bug than your hardware, even though that conclusion could be drawn due to you having a lowend system.
I'm just saying that it makes no sense that you could comfortably (even if it is at low settings) play out full games, even when it gets intense on the PC when there's 10 Demigod's, and a slew of fully upgraded creeps and towers with all their related animations popping off, then crash out within 10mins of an online 1v1.
Look into it at least, rather than putting it down to your computer, Demigod is not that intensive graphics wise, so you could also try turning all your settings to the lowest, and putting on a really low resolution then trying to play online, that'd prolly tell you.