Sounds like you have some really good transferable skills.
A good way in for business change project management is to start in a programme/project management/support office as a project co-ordinator / project analyst type role.
Expect lots of humdrum admin but also the opportunity to support project managers and hence learn project management practices. Often in large business projects other opportunities come up to then take on junior project management responsibilities.
If you want to get some training, Prince2 is a reasonable way in and the Prince2 Foundation certificate is pretty easy to get. It helps with the terminology at least. No formal training alone will get you a PM job though it may help prove your interest to get a role where you can learn on the job. Particularly when agencies are filtering out CVs. Also look at APM foundation level certificates or PMI.
Skills you need in a PMO role - organisation, planning, meeting facilitation, risk and issue management,budgeting, ability to deal with conflicting and changing priorities, often need to be slightly flexible in working hours as deadlines loom.
In more middling PMO roles the interpersonal skills become more and more inmportant as you spend time trying to influence people a lot more senior than you to do their boring reports right and adhere to the standard processes!
Good MS Excel, Powerpoint, Word skills are a real advantage. Likewise MSProject. I love finding an excel formula and macro whizz in a PMO team as so many things you end up doing revolve around collating, analysing and presenting information to various mgmt audiences.
My background: I started in IT but moved swiftly to more business oriented programmes. Now a freelance PMO management / project management consultant mainly in financial services but also have done public sector, telecomms, defence. I'm not techie at all but I can understand and work with techies! Most of my programmes have an IT element but we would employ people with much more specific skills for IT project management roles.
Hope that helps. I have to go on a conference call right now but if I remember I'll post some sources of info that might help.
Be aware that project management can mean very different things to different sectors. Take each job ad on its merits.