Worked on friend's bike. Now kinda wishing I hadn't...

I think you've given a warning to all of us who want to help out.

Let us know what it was in the end!

I would also be surprised if the chainrings aren't knackered after turning a chain that worn...

Is the rear mech 'b-adjustment' screw (think 105 mech has one?) set okay?

Also, I had similar issues (not 105 but Shimano Deore IIRC) where after changing rear cassette and chain, with good chainrings, still had a jumping chain in some gears - definitely from the rear.

Rear mech adjustment was perfect and gears would shift nicely when spinning the pedals by hand with the rear wheel off the ground, i.e. unloaded. When loaded however it jumped some but not not all of the time.

In the end I decided that although it 'looked' and shifted fine, the rear mech bushings were probably quite worn due to its age so bit the bullet and replaced that too. In my case that did the trick and it was only when I had the old and new mech's next to each other that I realised just how much the angular alignment had moved on the old one. The rear derailleur is obviously not loaded under pedalling forces but the interaction between it and the partially loaded chain must be different enough when compared to an unloaded shift test to subtly change how it is tensioned.

Hope you get it sorted. The bike too.

No comment on the chain wear rate

but

GET YOURSELF SAFELY OUT OF FRIENDZONE BRO !

The lift test is really to test if a chain is worn for those that don't have a chain checker tool.

I check for chain ring wear by pulling the chain at the bottom of the ring as it heads back towards the cassette, you will notice if the chain sits neatly into each tooth profile, or if you can see increasing amounts of daylight where the chain rollers sit in profiles as it wraps around the ring. As you know your chain is new and thus the correct pitch, it should sit in each profile all the way round the ring with no daylight when you pull back hard on the chain with your hand.

I also try lifting the chain away from the ring with just the top part still engaged on the top part of the ring, then whilst pulling on the chain, slowly wrap it back onto the ring. It should just drop neatly into the profiles, but if it starts to foul and catch on the teeth points or near the front edges of the tooth,as it wraps further around then the ring is showing wear.

If you have changed the chain, cassette, and free hub for new parts, then its either there isn't enough chain tension(look at chain length then derailleur tension) or the front crank teeth are worn. Need to work out if its front or rear jumping. Why don't you ride the bike and see if you can provoke the condition.

First thing is to establish where the chain is skipping. I usually put it in a heavy gear and give it a hard push from stationary, and watch the chain on the chain rings to see if it skips over those teeth. If it skips but not on the front, then repeat whilst watching the chain on the cassette. I sometimes get the owner to ride it whilst I ride alongside watching the drivetrain to see where the fault is.

From what you have said, it does sound like chainrings, some of the lower end Shimano original rings are made of butter, and do wear quickly if the chain gets badly worn.

You need to establish where the problem is before buying new parts.

Did you check the chain length on the new chain/chain set? That can cause skipping on all gears.

Well it's up to you if you want to keep on trying or give up.

Personally you've come this far you might as well keep trying.
Chainrings next!

Does it slip/happen in all the chainrings?

My theory: She is sabotaging the equipment so it keeps you visiting or she generates 1000 Watts and wears the parts out very quickly.

You probably did a good job but something is still wrong and from what you said, the parts needed changing.

Other people will 'put others down' and don't know anything or to impress a lady. Or they may have spotted something?

First diagnose the cause instead of throwing money at it.

One way to do this is to use a donor bike.

Swap the wheels, is the fault gone? Yes? Sorted it's the cassette or freebhub.

No? Then could be chainrings or chain or front mech.

I'd swap parts rather than buy but not everyone has a donor or compatible parts to try.

Check the chainrings or frame and if no luck then get a 3rd opinion.