Both of your Senns will sound much improved with proper amplification. You can also get custom cables to replace you broken ones, or order a new 650 cable from Sennheiser. Most will say that the 650 cord is better than the 580 cord.
Amps, or external DAC + AMP. Not sure where to point you except to the search function on this forum. There are many threads where folks extol the virtue of their amp with the HD650.
If I was starting over, I would get the "micro stack" from Headroom, with a DAC, and separate AMP. You can spend a LOT more, or some less. There are indeed several reputable DIY (do it yourself) amp makers here, and a bunch of supporting audio gear dealers here. You can also find some all in one USB DAC/AMP which will put what you are listening to to shame in a hurry.
Do some searching, search your wallet for a budget, and read read read here.
Oh, and the standard - "welcome to Head-Fi and sorry about your wallet!"