New drivers won't help within that stage of boot...however, motherboard firmware updates might. Firmware should support basic video functions compatible with most any video card, it isn't like this stage of boot needs to support anything proprietary.
It is also possible that the video card is bad, or that BIOS/UEFI settings corrupted. When was the last time you replaced that button battery on the board? Replacing that and using whatever jumper instructions there are for resetting BIOS/UEFI could help if something corrupted.
Also as a test you might try to boot with only one memory DIMM installed...be sure to use whatever slot the motherboard recommends for single slot memory use. If that DIMM doesn't work, try another, one at a time. This way you depend only on a single DIMM being functional.
FYI, if power is insufficient it will stop the BIOS/UEFI from functioning correctly, but the 1050ti does not take much power and BIOS/UEFI always runs at slow clock speeds, so it seems unlikely. The button battery seems much more likely if it is old.