You system needs some work.
I have a GTX 670 in my dad's computer and I sold the other one off before the Ethereum mining craze happened. For as old as the GTX 670 is, it's still capable of 1080p gaming.
The GTX 1050ti would be able to keep up with the GTX 670 but it's not much, if any faster. It looks like they're well matched aside for the 1050ti having more video RAM. It wouldn't be a suitable upgrade if you're asking for more performance. The link compares a GTX 960 to the GTX 670. The 4gb GTX 960 performs the same as the 4gb GTX 1050ti.
You're looking to go up to the RX 570 or 3gb GTX 1060 level at the minimum. Unfortunately thanks to the mining craze cards like that are in short supply. You can use nowinstock.net to find cards, which usually go very fast. I can't recommend getting a used GTX 970 because the prices of the used ones on ebay have increased over 50% within the last 6 weeks. There is a serious graphics card shortage.
A few other points.
Even way back then in 2012 the Core i3 wasn't considered a real good match for the GTX 670. I can't imagine what kind of bottleneck you're seeing with today's games. Back then a few games got hamstrung by that Core i3, but now that's become worse. You can upgrade the CPU to something like a non-K 3rd Generation Core i5 or i7 CPU like the Core i5-3570, 3550 or 3470. Even a Core i7-2600 would be a far better option than what you have. The 3rd Generation Core i5 processors go for a pretty low price on ebay. You would have to update the BIOS if you went with a 3rd Generation Intel CPU. If you tried to match your COre i3-2130 up with an RX 570 or GTX 1060, you would definitely see a bottleneck.
4gb of RAM is not enough for any current games. You need to have 8gb of RAM at the minimum. If you do decide to upgrade to a 3rd Generation Intel CPU then look at DDR3-1600. If you decide to upgrade to a Core i7-2600 then DDR3-1333 is the most that CPU can handle at stock speeds with your locked h61 motherboard.
The power supply you've been using is barely sufficient for the GTX 670 and at least 550w was recommend for that card. The reason is to give you overhead and account for the shortcomings of lower quality power supplies. That 430w power supply would work fine with a GTX 1050ti but it would be just barely enough for the 3gb GTX 1060.
Power supplies lose their capacity to supply power over time. The Be Quiet power supplies aren't known for being ones of high quality. Some of them were made by HEC which isn't a good company. When you were gaming, you were likely pushing over 275w which is pushing a budget power supply like that to it's edge. I would recommend looking for a quality 550w power supply before venturing off into upgrade land. It wouldn't shock me one bit if that power supply is the reason your GTX 670 is now dead.
https://www.asus.com/Motherboards/P8H61M_PRO/helpdesk_cpu/
https://www.techpowerup.com/gpudb/2885/geforce-gtx-1050-ti
http://www.anandtech.com/bench/product/1769?vs=1744