Ping is not local. Singleplayer won't lag because your internet connection is bad. The FPS is determined by your hardware or drivers. The internet connection lies beyond your PC. If you get more than 160 ping all the time, you should connect your ISP's Support service. Other games can get good FPS with outdated drivers, but especially if you have a Radeon card, it makes a difference to Toribash because of sucky OpenGL support in old versions. If you used to run Toribash better with the computer you're using now, it's because of the drivers.
See, the internet connection means how long your PC uses to send data to other computers, not how fast it computes itself. Summed up: FPS has absolutely nothing to do with internet. I still recommend updating drivers to the very newest, it will never be negative, and will improve performance overall anyway.
I cannot recommend a new internet, because at the moment, we only have one proper worldwide internet. I can recommend contacting your internet service provider and tell them about the problem. If they don't know how to repair it, you really should find a better ISP with a better crew for technical support.