There have been instances where I observed a new spot in TLC plate and have isolated it via Column Chromatography.But it could not be characterized even after obtaining data for 1H, 13C and DEPT 135.
Combine it with other methods too. Mass Spectrum can be analyzed also, to provide valuable information on your new compound.
Make sure to anticipate what you synthesize, also the biproducts. If you have any clues prior to an NMR analysis, it will be much easier. Simulated spectras can be generated for possible compounds and this may lead to your final conclusion.
Otherwise, if the compound is somewhat medium sized or small, it should be possible to identify it using your mentioned methods, 1H, 13C and DEPT 135.
Although you probably know, there are a few more NMR methods you can also apply which may help, especially 2D, such as COSY/HETCOR,
If it is a synthetic compound you can just compare the NMR spectrum of your compound and find out the difference and you will know what are the changes and on the basis of these changes you can find out the structure.
In case of natural products first you should know the class of compound from the TLC spot upon using different reagents for visualization. Then of course you will need different spectroscopic techniques not only nmr but mass, uv and ir too.
I shall agree with the comment by Mr. Glud, that for unknown substances the structural information can be obtained by MS. In particular, when we are talking about complex molecule, which currently are of much great interest, comparing with small molecular weight objects, which generally do not represent any difficult both employing NMR or MS.
Towards prediction of NMR spectra from a hypothetic structure and vise versa, there have been met series difficulties even in-front most recent theoretical approaches for an accurate prediction of shielding tensor components and coupling constants employing ab initio treatment of the electronic structure. In addition to the fact that when flexible molecules are objects of analysis, there are set closely disposed as energetics conformations (DE < 6.10-4-6.10-6 hartree), which accuracies are higher then the uncertainty of 3D structural information received by experimental NMR. It is about 1 - 4o of the dihedral angles. This means, that difference of 1-4o in the dihedral angle, which is uncertainty of the experimental 3D NMR can correspond to set conformations of the molecule with close energies. They shall be distinguished in energetics terms, theoretically by quantum chemistry, yielding to corresponding NMR data, but not experimentally by NMR. In other words you have not unambiguous information using NMR when a complex and flexible molecule is an object of analysis. And this is, first. Second, you have not absolute information as well as.
So...MS has much greater advantages and a smaller number disadvantages comparing with NMR like costs; sample amounts; pretreatments steps; efforts in interpretation; detection limits both concentration and instrumental LODs; and more, studying unknown compounds!
Towards the software mentioned in your second posting, there is much better the ACD Labs (http://www.acdlabs.com/).
If you have, in particular, interest from a database-use for prediction of a structure, again MS based databases have greater advantages due to set instrumental and techniques specifics of the MS as characteristics of the methods/instrumentation.
I do agree with Murad Ali Khan. To begin, you should at least know the class of compound the unknown dealt with comes under and the related NMR property particularly for bigger molecules. For synthetic products, you should know your starting materials and the expected products. However, for an unknown natural product, you will need to do a series of test to obtain this information such as tlc, chemical test, infra-red spec. uv-vis. etc. Without knowing the spectral information of the base structure of any class of compound, the task ahead may not be easy.
I do not know the amount of unknown sample you have, but in my opinion before use mass spectroscopy you can use a infra-red that will give information about the functional groups presents in the molecule. Its will help you to analyze mass spectra and NMR too. Before send your sample to get any spectra, be sure that that it is dried and free from any kind of solvent.