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Yes, you can absolutely contest it. Note that you can't just "contest it" based upon you being left out of the will. It was her right to do so assuming that she had testamentary capacity.
To make a Will or other testamentary document (something happens at death, rather than right now), a person must have “testamentary capacity.” A person has testamentary capacity if at the time of the signing she (1) knows those persons who would naturally have some claim to her remembrance; (2) comprehends the kind and character of her property; (3) understands the nature and effect of making a Will; (4) and is able to make a disposition of her property according to a plan formed in her mind free from delusion which might influence the disposition of property.
Furthermore, it would still need to be within the requirements of a will (signed by the testator, witnessed by two witnesses) to be valid. So a will contest either challenges the capacity of the testator or the form of the will. To be successful, you would need to win on one of those element.
That being said, you need to contact an attorney in your area that deals with probate / will contest cases. Go to www.lawyers.com or www.legalmatch.com to find an attorney in your area. You should be able to find one that will give you a free initial consultation and better advise you of your rights, any problems with your case, likelihood of success, how courts are treating cases such as yours in your area, and what you should do next.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for my answer unless and until you rate it a 3, 4, 5 (good or better). Thank you, ***** ***** luck to you!