How do I find out the REAL date of last payment?

How did you make the payment? If it was done by check, you will find the entry in your bank statement. If you used money gram or western union, you must have the receipt showing the date on which payment was done. Aside, you can always confirm it with Sears. Dispute in writing if the date you have doesn't match with their date in the system. You will need proof from your side to make your dispute look correct.

I'm afraid I probably don't have any kind of payment record. I wasn't as savvy then as I am now. The guy at Weltman, Weinberg mentioned he could see all the collection agencies that this account has been too. If that is the case, he should be able to provide that to me along with any kind of payment that has been made, right?

Get the debt validated by this Weltman Company. They will show you proof when you did the last payment. You don't have the payment record but you might remember the bank where you had the account. You should be able to pull duplicate statements.

You don't remember whether you made a check out or paid with a money order? If not, I would recommend that you contact the company and request a statement for all of your payments. I would also recommend that in the future you keep documentation when dealing with companies such as these.

If you paid via money order, there should be a telephone number on the money order. Call that number and they will be able to tell you when the money order was cashed.

My suggestion would be to contact CitiBank since they own the Sears cards. I've worked briefly on the Sears project and it is true, at least on our system that you can not see the last payment made.