Unless ridiculously steep, you can make most hills in 3rd or even 4th if moderate.
The AA or RAC would almost certainly look at fuel/spark first if vehicle has been ok up to then but in this instance (with an unknown) you have to glean what power might be available if fuel and spark were functioning correctly. A compression check will tell you that quickly.
Otherwise you can (as many often do) end up replacing stuff in the hope that its this or that and not have a clue. I know of serveral 80/90 members that have tackled issues that way and their bill has run into several hundred pounds. Its just not the way to do things. Start from the bottom up and you should find the cause. Work from the top down and you can quickly run out of money as well as the will to live.
As Joe Friday would say: "Just the facts, ma'am"
Could be running on 3, badly timed, starved of fuel but best to know if its capable of delivering power under load to start with. If it is, we can work through everything with you, bit by bit.