If any plant breaks down & rots within a 2 week period, then I'd hazard a guess that they are non-aquatic.
Believe it or not, many LFS sell non-aquatic plants as aquatic BTW.
To grow plants they need:
Light
CO2 (if you have more than about 2W/US Gal, CO2 imh should be from a gaseous source such as injected or DIY yeast)
Primary (NPK) & Secondary Macro Nutrients
Mirco Nutrients or 'Trace'.
To get the nutrients into the tank use something like SeaChem Flourish or AquaCare Plant Nutrition+ Liquid (formerlly TMG+).
If you live in a softwater area also consider using SeaChem Flourish Equilibrium.
For a source of CO2, SeaChem Excel can be used (I'd only use it if lighting >1.5W/US Gal).
Andy