burnt wire terminal on infinite switch

Electric Cook top burner failed to heat.
Traced to bad infinite switch.
When replacing switch, found burnt, fragile terminal on wire. Terminal on infinite switch was burnt and separated from switch body. Attached burnt wire terminal to new switch, hoping it would work; and still does not work.

Do I need to replace entire (yellow) wire (part of main harness) or can the wire be spliced?

Thanks!