Consider a number of I(1) processes that are cointegrated so that their linear combination is stationary. (Higher orders of integration and cointegration are straightforward to generalize to).
When testing for cointegration using the Johansen or the Engle-Granger tests, original series (rather than their first differences) are used.
The dependent variables of a VECM are the first differences. However, the software will normally require to input the original variables for estimating a VECM -- check the documentation carefully.
All of this can be found in any modern time series textbook (e.g. Lutkepohl "New Introduction to Multiple Time Series Analysis" (2005)) or e.g. here (there are more good online resources, just search for "vector error correction model").
Also note that in economic and financial applications it is normally enough to difference the data once to achieve stationarity. If the first differences of your data are nonstationary, perhaps your data is not only integrated of order one but also contain structural breaks or other "unpleasant" features. Differencing more than once need not be the best solution then.