2 weeks ago during the Christmas/new year holidays, department head emailed me saying HR should send me the official offer sometime early in next month, but here is most of the information (salary, tentative start date, etc etc). Of course, i replied saying thank you and everything looks good and can't wait to start. But, now its been three weeks into the month, and nothing. I emailed the HR, but no reply. So, should I consider this "verbal offer" rescinded by now. Or wait for few more weeks, before accepting the defeat instead of the offer! It is a very large company with big HR by the way, and i won't be starting until summer, at the least.
HR is not your friend so don't act as if they are. Nobody is sitting there and saying "Oh my! We haven't called sdd!!!". They are just operatives for the company.
Call them for a follow up. This is too important to leave in email. HR likely gets hundreds, if not THOUSANDS of emails every day. Yours can get pushed down to the bottom, caught in a spam filter, of seen and forgotten.
CALL THEM or you might miss the opportunity
Most definitely reach out to the company.
If the offer is still on the way and has been delayed, you reaching out and showing interest and investment in getting this position isn't going to change their mind about you and rescind the offer.
If they did decide to go another direction, then you know and you can continue looking.
It's the not knowing that is the worst part I would think.
Contact them and find out. Ask them if there are any issues, as you were concerned that the offer has been lost in the post (maybe it has?)
Big companies can forget, 2 weeks can turn into 2 months, especially if you'd be starting in the summer.
Worst case scenario, at least your not left wandering what the situation is.