TurboTax's Wisconsin state tax product is not as intuitive as it could be.
First, I will answer your question simply and directly: In your situation, enter $0 here. You do not need to enter a negative number. In future years when you are asked this question, you will also enter $0. For the other boxes on this page, also enter $0.
There are 3 boxes on this page, and TurboTax requires the second box to be less than or equal to the first, and the third box to be less than or equal to the second. If you end up with a negative number for the first box, enter a $0 for all three boxes.
Now, here is the explanation for this confusing section, for anyone that had an HSA in 2010:
Before 2011, Wisconsin did not recognize the HSA. If you put money into your HSA, you deducted the contribution off of your federal income, but you had to add the contribution back into your state income on Wisconsin's Schedule I. Starting with the 2011 tax form, you didn't have to do that anymore, as the contributions were just as deductible on your state income as they are on your federal income.
Here's the issue: Let's say that you had some money in your HSA in 2010, and then withdrew that money in 2011 for something other than medical expenses. On your federal return, you would have to add this back into your income to pay tax on it (as well as a penalty). However, Wisconsin wouldn't tax or penalize that, because you had already paid tax on that money in the year you put it into the HSA.
As a result, TurboTax wants you to look at your HSA balance at the end of 2010 and then subtract any distributions (withdrawals) from your HSA after that point through the end of the previous tax year (in this case, the distributions of 2011-2014).
If you still have a positive number at this point, it means that some of your distributions from this tax year (2015) are attributable to your pre-2011 HSA balance. Here are the implications for 2015's distributions, up to this amount:
If any of the distributions were not used for qualified medical expenses, you don't need to add that back into your state income, nor do you need to pay an extra penalty for the state.
The portion of the distributions that were used for qualified medical expenses can be used as an itemized deduction when computing the Wisconsin itemized deduction credit.
Eventually, the total of your distributions over all the years since 2011 will cancel out your pre-2011 HSA balance. At that point, you don't need to worry about this anymore, as your non-qualified distributions will be subject to state taxes and penalties, just like the federal taxes.
Wisconsin has a fact sheet about HSAs (pdf) that explains this in a little more detail.
Back to this Wisconsin TurboTax page:
For the three TurboTax boxes on this page, all of them have misleading descriptions.
The first asks: "Value of HSA(s) on December 31, 2010 minus any distributions in 2011, 2012, 2013, and 2014." What they also need to explain on here is that if the value is negative, enter $0.
The second asks: "HSA distributions in 2015." However, what they really want here is the "HSA distributions in 2015, up to a maximum of the value in Box 1." That would be the 2015 distributions that are attributable to your pre-2011 balance. This number needs to be less than or equal to your Box 1 number, and if Box 1 is $0, this one should be as well.
The third asks: "Amount of 2015 distribution used for medical expenses." Again, they really want to know the amount of your Box 2 distributions that were used for medical expenses, and this amount needs to be less than or equal to Box 2.