If you simply redirect your old domain to the new one, you will simply be transferring all the bad links from one domain to another. If you are starting fresh with a new domain, you shouldn't be using 301 redirects.
An aged domain can sometimes retain some authority, but if it's been parked for a while, probably not. If the domain does not have any active links coming into it, then just the fact that it's old does not mean it's going to rank well. Best to just pick a brand new domain that's a better fit for your brand.
