Absolutely not too old! In my office the office juniors range from 16-year-olds to 21-year-old graduates. The key is that they are all willing to do the crappy jobs - and may well want to work their way up but do some hard graft on the way. No boss could knock someone for being honest about that.
Also, in this day and age, with so many people staying on in education till a later age, the age of office juniors has risen. Being a bit older could work to your advantage - you will hopefully be a bit wiser than a younger candidate!
After graduating at 21 I worked in a variety of jobs - from working as a filing clerk to cleaning toilets (seriously!). This willingness early on has helped me to get other jobs - nothing says 'I don't mind working hard to succeed and get a job done' than admitting in an interview in your 30s for an executive position that you once cleaned toilets for a living. Always gets a smile out of the sternest interviewer! And shows you are not too proud!