We sold and bought a new home in 2017. We lost all records regarding the purchase of the house in Illinois. How do I figure the profit of the home in Illinois?

Since you sold your home in Illinois for less that $500,00, you will not have to report the sale if you are Married Filing Joint.  Even if you used $0 for your cost, you are  still under the exclusion if you qualify (see below). If you don't qualify for the exclusion, you can usually find your purchase price on the county property appraisers website. If not, then call the property appraiser.  

The IRS has a provision that can help homeowners avoid capital gains on the sale of their primary residence.

To qualify, you must have owned your home and used it as your main residence for at least two years in the five-year period before you sell it. You also must not have excluded another home from capital gains in the two-year period before the home sale. If you meet those rules, you can exclude up to $250,000 in gains from a home sale if you’re single and up to $500,000 if you’re married filing jointly.

If you sell a home that was not a primary residence or that does not meet the above requirements, then you would pay capital gains on that sale.