its an intel i3 that's about all i know
I can say i3 can't mine anything unless you are lucky boy. My i5 only hit 1 block in more than 48 hours.
how do i connect this to my wallet?
If you use win, it's easy. And slimcoin.conf file in your Appdata/Roaming/Slimcoin/
And the nodes in you slimcoin.conf which you can find in this thread by searching the keywords "nodes".
how do i know when i've actually got a block that's worth money?
Type "listtransactions" in your wallet's command line.
If you want to mine, type "setgenerate true -1"
If you want to burn, click Burn coins, and input the amount you want to burn.