FWIW, if you're looking all over the place for an internship, maybe don't rule them out[1]. Often companies lay off employees who aren't useful to them, but are still looking for employees who will be useful. In particular, someone who's good at programming[2] and junior[3] might be the kind of person they still want to hire.
[1] Then again, the fact you're commenting on HN probably means you're a strong candidate who'll find an internship with ease. So follow your dreams. ;)
[2] Again, just assuming this based on the fact you're an HN reader. You might be horrified to see what proportion of people in a BigCorp company can't do even basic reasoning.
[3] Pay an intern pennies to do pounds worth of work! Yay!
I don't know to what extent this is a problem at IBM, but I've seen a few places where it is a huge problem. And I agree with you. The "yay!" was sarcastic.
I interned for IBM twice: once in '95 (Boca) and once in '00 (Hawthorne as a research intern). The second was by far much better (working with all those great researchers), but there is just something about working for IBM that is a bit depressing...it really is Big Corp.
My current employer (Microsoft) has a reputation...but the reality is no where near what I felt when I was at IBM.