It is near-on impossible to get a career in the Music Industry and I'm speaking from experience...
For two years, I've applied to hundreds of different companies, radio stations, tv stations, recording studios, publishing companies, royalty agencies, Musicians' Union etc etc. The reply from all of them is the same - it's hugely hugely competetive and there are rarely any jobs available. They all said that it's a question of getting your foot on the ladder, i.e. getting a job as a tea girl or postboy etc and 'networking' to gain essential experience and promotions within the same company. Initially I took the rejections quite badly as I feel I'm a good candidate - MASSIVE interest in Music (Classical, Mainstream and Alternative), straight A's, am doing a Music degree, play four instruments to grade 8, three years retail and Customer Service experience, previous work in admin, speak French fluently alongside basic German etc etc. The point is, it's not a question of calibre, it's a question of luck.
Again, the few posts that I have been offered, as 9 to 5 admin assistants and secretaries at Music Publishing firms are all UNPAID. Sadly, they don't even pay expenses and I couldn't afford to pay three months of London travelcard. It's a vicious circle, however, as if I took these posts, I wouldn't be able to take another part-time job to pay for it, as nearly all my time will be taken up with the unpaid work experience.
Unsure2 and Mendelssohn are exactly right - BMG also made thousands of employees redundant the other month, due to losses from the Internet market, so the Music companies just aren't looking for people. As a result, my long term plan is to move into Music Research once I graduate. My other option is to become a freelance harpist, which has always been a major source of income for me since I began at University.
Either way, Music will be a precarious and dangerous career path as it's non-essential and non-vocational. People with law degrees and medicine degrees have the pre-destined path as a lawyer or doctor, whereas musicians have to fight for the few posts there are that are related to their degree.
Basically, it's not a good time, as everybody else has said.