Hi, the only part that dont have the circuit under neath is the part that has broken off the only chance you might have of finding somewhere to drill through is if you take the key apart and have a look on the inside and see if their is a small gap you can drill through.
if you just drill through without taking the case off you will never know whats under neath, now with the case off you may find a small part near the back of the key next to the part that broke off but it will only be a small area, so if you take the case off and drill a hole you will probably need one of those straps that go through a mobile phone, you know the string type that you feed through the hole on a mobile well you may be able to drill a small hole big enough to put this string through, but you wont be able to drill a hole big enough to put the metal ring through on its own.
if you can get the case off without damaging it then have a look at the back part near to the part that broke and you should find a small area to drill through, please dont drill anything without taking the key fab apart as you will drill through the circuit, its not worth guessing as damaging this could mean your car wont start.
failing that replacing the key is the only option
take the case off and have a look first just take your time and try not to break anything inside the key, if you have messed about fixing things before then you should be able to take the case off the key.
let me know if you need further assistance ok
CAUTION: Prior to removing center pins from the rivet, it is recommended that a suitable block support be inserted between door outer panel and glass bracket to stabilize glass during rivet removal. Remove center pin from each rivet with a drift punch. Using a 1/4-inch diameter drill, drill out remaining rivets as damage to plastic glass retainer and spacer could result. 
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