What services? Services are generally things people want done but don't want to or can't do themselves. In a star trek world I would expect these things that are still relevant (e.g. tax support services and the like obviously wouldn't exist anymore) would be handled by robots, which themselves are made by the replicators.
There would still be things to do of course. But they would be things that people want to do and wouldn't need to charge for since they no longer have rent or food/utility bills to pay.
Right now, if we look at just music, there are some people in music because they love it and it's their life. There are many more people who are there because if they make it they'll have insane amounts of money. But pretty much no one can do it for free because everyone has to buy food.
If there were no more money and no more bartering, only the first group would stay in music and they wouldn't need to be paid for it because they wouldn't need money.
I expect things like real TV would go away because that kind of stuff is mostly to push advertisement and without money what would you be advertising?
This works only if the two nodes in the network have exact matching needs/abilities. This is rare even in small groups.
If you will, money is a message is a message passing protocol. I don't care what's on the other side and how the message (money) was generated - all I care is that I received a message (money) and then I sent other messages (money) to other actors in the network (obviously I sent back something in exchange and so do the other nodes). Then they generated their messages and so on. This way all I need to know are the nodes immediate to me to work it out. I don't care how complex the message graph becomes, it's all irrelevant to me and to others as well. If you don't have that then you have to broadcast all that you offer and all that you need and somehow create the graph to work it out all out. Money is a cheap way of abstracting all that.
That's not post-scarcity. That is inefficiency. And it is still capitalism. Money is a bookkeeping system for IOUs, not an economic operating structure.
Even under barter and trade, there is profit. To go with the GP's example, one persona valued having his trees pruned more than he valued the time he spent upgrading the computer, and vice versa. Both parties profited and ended up better off or else they wouldn't have made the trade.
The lack of money involved just makes it potentially less efficient if the trade isn't well balanced, or potentially more efficient if they can avoid the friction of the taxman by avoiding money.
Services. Goods aren't the only resource one pays for. Peoples time and energy will still be scares.