The professor I am trying to contact has multiple email-ids listed on the department page. I mailed to one and got no response sice two weeks, then I mailed to the other and still no response since a week. I was wondering if he was receiving my emails at all and I decided to check more into the department page and found out that it hasn't been updated for about a good 10-15 years. All the student lists refer to people who passed out decades back, this made me think that the email-ids listed may also be outdated. His recent papers show a different email-id, at this point I am in a bit of a fix, since I don't want to sound rude by pestering him with emails (if he indeed did receive it and chose not to reply) but at the same time I'm not sure if he received them at all? Would it be good idea to mail him at his most recently used email-id?
Yes, write again to the most recent (as mentioned on publications) email address. If you worry about making him feel like you are spamming him, explain shortly that you tried the what you think are old emails first, but then found this (now used) address. The old "excuse for double posting" might also work in slightly changed wording.
You cannot expect someone to check all old email addresses, especially should those be from a different university. Of course it could be that all your emails were forwarded or are connected to the same mailbox, hence you might want to include a short note explaining your potentially multiple emails.
This is highly appropriate; professors get bombarded with e-mail and often thing's slip through and e-mails change (although I still get e-mail from most of my old e-mail addresses-- doesn't mean I respond to all!). By repeatedly trying, you are showing perseverance and a true desire to get in contact. Be polite, explain why you desire to get in touch, be formal (no Dear Tom, if you haven't met), and be nice. If the professor thinks it spam, they will let you know. IMO.