How can I drill out this remaining piece of screw?

A quick learner from Central Florida says:
Hello Tom,

I have a set of doors where the bottom frame screws have broken off. I have been unable to get a an extractor to drill into the remaining piece of the screw. It looks like the door frame screws are turned into a slot in the aluminum. How do you suggest I remove the broken screw?

I am thinking of using a Dremel cutting wheel to split the screw and then pick it out. Your thoughts are appreciated.

Best, Tom
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Dave Sr. from SWISCO responded:

I have had this problem in the past, but yours has been compounded by the corrosion in the door frame. That is a big hassle, but I will do my best to help you get through it!

What you need to do is to first lubricate the broken screw to loosen it up in the frame. Try a WD-40 or Liquid Wrench. Give the lubricate some time, maybe a day or two, to sink in. Place the door channel into a bench vise to hold it in place while you do this. 

Next, take a slotted screw driver and spread the screw channel in the door frame a little. Then, get a center punch or a scratch awl and use a hammer to drive it under the broken screw. That will hopefully lift it out of the screw channel. You might need to finish the job with a set of pliers. 

After the screw is removed, use your pliers to squeeze the channel together again to accept a new screw or use a longer screw. To be honest, using a stainless steel screw to put the frame back together and might be best to replace all screws at this time.

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