Is it possible to access my MarketDelta from both my desktop and my laptop at the same time?
No, you can only be logged in on a single computer at once. This is mandated by the exchanges because you are paying 1 set of exchange fees. You can install the software on both computers and when you load it up on one it will gracefully close the other one down and let you login on the other.
One alternative solution would be to have your broker provide you a second login enabled for "MarketDeltaCloud". There would be a $25/month data fee plus exchange fees, but this would provide a low cost way of logging into your same trading account from your laptop AND be logged into both applications at the same time.