The Intel Z77 chipset was for the LGA1155 socket. That was compatible with Intel Ivy Bridge
and Sandy Bridge
processors sold between the beginning of 2011 and the middle of 2013. Those old systems use DDR3 memory.
If you're sure that your dead pixels are on the graphics card and not the monitor and all that you need is a new graphics card, a $170 GeForce GTX1050Ti 4GB
or $150 Radeon RX 570 4GB
graphics card should work with your old PC. I do not recommend a new gaming graphics card with less than 4 GiB of video memory.
If you want to upgrade CPU or motherboard or system memory, you will need to replace all three of these components together.
One example would be to match a socket AM4 motherboard with the AMD B450 chipset (e.g.: $85 Gigabyte B450 Aorus M
AMD Ryzen CPU (e.g.: $160 Ryzen 5 2600, including heatsink & fan),
and 2 each 8 GiB DDR4 DIMMs for memory (e.g.: $105 DDR4-3000
Those pieces total to $350.
A combination using the same memory with a $275 Intel Core i5-9600K CPU, $30 Arctic Freezer 13CO cooler and a $125 ASRock Z390M Pro4 motherboard would cost $535.