Backup & Transfer my emails to a new laptop -- 2

Kind of support: Email Description of support work: I am looking to transfer my email programme - Incredimail - [login to view URL] from my old laptop - Windows 7 Home Premium 64 bit to My new Laptop - Windows 8.1 64bit I have tried various incredimail backup/transfer programme but due to the matter that i have around 28,000 plus emails (approximate guess) 28gb plus (approximate guess) it crashes when backing up. I have two choices. 1) Backup and transfer my emails (Somehow?) to the new laptop. 2) If this is possible. - Back up my emails and have them on my own private hosted server/cloud system. My email address is my first name and family name of which I purchased the domain from [login to view URL] Other Information: All emails are in ".eml" format. I am open to other suggestions if anyone has any better ideas, the main point for me is to be able to get all my emails off my old laptop, safely and proceed with one of the options above Remote access will be granted to the awarded person and as this will take sometime, I expect them to start the process and check back as and when required and not spend hours watching it back up. The agreed price on the start of the work will be paid when the work is fully complete. Please contact me if you have any questions.