Ruby, 1068 bytes
require"zlib"
require"base64"
$><<eval(Zlib::Inflate.inflate(Base64.decode64"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"))[gets.downcase[1..5].to_sym]
Input via STDIN.
The shortest unique substrings of the element names are from the second to the sixth character (or the end of the name if its too short). So I'm simply getting those and looking them up in a hash. I also compressed the hash because that saves another 200 bytes. Here is what the hash itself looks like:
{ydrog:?H,elium:"He",ithiu:"Li",eryll:"Be",oron:?B,arbon:?C,itrog:?N,xygen:?O,luori:?F,eon:"Ne",
odium:"Na",agnes:"Mg",lumin:"Al",ilico:"Si",hosph:?P,ulfur:?S,hlori:"Cl",rgon:"Ar",otass:?K,
alciu:"Ca",candi:"Sc",itani:"Ti",anadi:?V,hromi:"Cr",angan:"Mn",ron:"Fe",obalt:"Co",ickel:"Ni",
opper:"Cu",inc:"Zn",alliu:"Ga",erman:"Ge",rseni:"As",eleni:"Se",romin:"Br",rypto:"Kr",ubidi:"Rb",
tront:"Sr",ttriu:?Y,ircon:"Zr",iobiu:"Nb",olybd:"Mo",echne:"Tc",uthen:"Ru",hodiu:"Rh",allad:"Pd",
ilver:"Ag",admiu:"Cd",ndium:"In",in:"Sn",ntimo:"Sb",ellur:"Te",odine:?I,enon:"Xe",esium:"Cs",
arium:"Ba",antha:"La",erium:"Ce",raseo:"Pr",eodym:"Nd",romet:"Pm",amari:"Sm",uropi:"Eu",
adoli:"Gd",erbiu:"Tb",yspro:"Dy",olmiu:"Ho",rbium:"Er",huliu:"Tm",tterb:"Yb",uteti:"Lu",
afniu:"Hf",antal:"Ta",ungst:?W,heniu:"Re",smium:"Os",ridiu:"Ir",latin:"Pt",old:"Au",ercur:"Hg",
halli:"Tl",ead:"Pb",ismut:"Bi",oloni:"Po",stati:"At",adon:"Rn",ranci:"Fr",adium:"Ra",ctini:"Ac",
horiu:"Th",rotac:"Pa",raniu:?U,eptun:"Np",luton:"Pu",meric:"Am",urium:"Cm",erkel:"Bk",alifo:"Cf",
inste:"Es",ermiu:"Fm",endel:"Md",obeli:"No",awren:"Lr",uther:"Rf",ubniu:"Db",eabor:"Sg",
ohriu:"Bh",assiu:"Hs",eitne:"Mt",armst:"Ds",oentg:"Rg",opern:"Cn",nuntr:"Uut",lerov:"Fl",
nunpe:"Uup",iverm:"Lv",nunse:"Uus",nunoc:"Uuo"}
Au
, or whatever you want. @Paul R If there are many ways to spell an element (e.g. sulphur vs sulfur or aluminium vs aluminum) use whichever makes your program shorter. You do not have to handle both cases. \$\endgroup\$