Prizm, sometimes starting, sometimes not

I have a 2002 Geo Prizm and its been a great little car, minimal problems with it, 109,000 miles on it. I just got new struts and brake pads on it, and every thing was fine, it was starting without any problems. It has a pretty new batter, Die Hard, that is about 9 months old. Then one day I try to start my car after work, and it doesn’t start. I just thought it was a fluke, maybe I left something on? So I jumped it, it started fine, I drove it around on the interstate for 45 min to charge up the battery. The next morning it started fine, but that evening after work it wouldn’t start again. So I jumped it again, although this time it took several attempts to get is started from the jump. The battery connections are tight.
I rented a car for the following week, so I can reliably get to work. And I was starting to think it might not be worth it to put more into the car. The car has been sitting for over a week while I have been driving the rental, and I decided to move it from its parking spot, figuring I’ll need to jump it, but I thought I would just try to see if it would start, and to my surprise it started right up and drove fine.
I had kind of resolved myself to the idea if finally having to get a new car, until today, when my old car seems to be doing better. Any idea what might be wrong? Would it be easy/cheap to fix? Or do you think this car has run its natural life?
thanks so much for your help!

This could be as simple as a bad battery, it happens with new batteries-that is why they offer a warranty. Try to get to the shop that put the battery in, or a McParts store (Advance, Pep Boys etc) Most of them will check the battery and charging system for free. You may have a trunk or glove box light on draining the battery, see if you can check those

This car hasn’t run its life by a long shot. It is essentially a Toyota Corolla with a Geo badge. The engine and trans are good for at least another 100,000 miles. You are having a typical problem with an older car. @SteveCBT is right, could be a faulty battery, could be a light being left on with a faulty switch or another component could be draining the battery. It could be corrosion under one of the battery cable connections - the ones at the battery or the other ends. Not an impossible problem to fix and certainly would cost less than even 2 months of a new car payment to have someone fix it.

A common problem on Toyotas is that the starter solenoid contacts get worn, giving an intermittent no-start. What, exactly, happens when you turn the key? Just a click, but no engine turnover? That might be worn contacts, which can be replaced with a kit like this:

Or you can replace the entire starter (you need to remove it either way).

Two other possibilities are the transmission interlock - does moving the shifter to “N” let it start? Also might be the ignition switch.

But my guess is the starter solenoid contacts, speaking from experience.

I tend to agree with @texases

Those Denso starters are known to get finicky, after a few years

One more vote for the advice provided by texases. I have repaired the Denso starter contacts in two Toyotas and one Plymouth. You might find a shop who’ll remove and repair the starter, but it may be more cost-effective for a non-DIY person to have a rebuilt starter installed.

Get the battery and charging system tested, as Steve suggested. If they’re good, it’s the starter.

When you turn the key to START, a subassembly of the starter (1) slides the starter motor gear into engagement with the flywheel ring gear, and (2) engages contacts to enable the starter motor circuitry to turn the motor. Those contacts wear over time, and are also subject to small arcs every time they engage and disengage, which “fries” the contacts. The arc vaporizes material, transfers material, and leaves carbon deposits. It’s minute for each event, but over time it makes the contacts intermittent.

As others have said, if this car is properly maintained it has many years of happy mileage ahead. This condition is not at all abnormal for a thirteen year old car. And it isn’t unique to Toyota.