The program is trying to determine the amount of contributions you made to the Roth IRA you cashed out. You can withdraw contributions you made to your Roth IRA anytime, tax- and penalty-free. However, you may have to pay taxes and penalties on earnings in your Roth IRA. You aren't being asked about your other Traditional IRAs.
FYI, even though you couldn't roll your Roth IRA into one of your existing traditional IRAs, you could opened a new Roth IRA and rolled it over to that account. There are multiple financial institutions where you can open a no fee Roth IRA.
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Employer-plan-based Roth accounts are not Roth IRAs and are not included in determining the taxable amount of a Roth IRA distribution. Employer-plan-based Roth accounts are instead designated Roth accounts in a 401(k), 403(b), 457(b) or the federal TSP. Designated Roth Accounts and Roth IRAs are different types of Roth accounts with different rules.
There is no reason that you could not have rolled over a Roth IRA distribution except in the case where the distribution was a return of contribution, either codes J and 8 or codes J and P in box 7 of the Form 1099-R.
Code J simply means that the distribution was paid to you and you were under age 59½ at the time. You could have rolled it over unless you had rolled over another IRA distribution made within the one-year period ending on the date of this distribution. Perhaps what you were told was that it was not possible to do a nonreportable trustee-to-trustee transfer, but that would not preclude you from rolling this distribution over within 60 days of the distribution.