Yes, which is a good reason to just replace the rings, either new rings or rings from a purchased crankset. From the pictures, do you have 110mm or 130mm BCD? Another option is to buy a used crank with good rings. Or a cheap 52/42 crank set with steel rings, and use just the rings until your money situation improves. For example: Silver Double Alloy Road Race Chainset 42/52: Amazon.co.uk: Sports & Outdoors

You definitely need chain, cassette and chain rings. Chain rings wear MUCH slower than cassette cogs.