If the house was bought for $12,000 in 1953, that basis transferred to the 3 siblings in 1994 ($4000 each).
You bought out the third sibling for $24,100 in 2004. Your basis in your half is $4000 + 12, 050 = $16050. Your sibling's basis is the same. You may add the cost any improvements (but not repairs) made over the years.
The gift was not taxable, but Mom's basis transferred to you. She shoulda filed a gift tax return, in 1994, unless each sibling's share value was less than the gift tax exemption amount (that was probably the case).
