I had one of these a while back and it seemed to suffer similar issues. Oddly, I still have an (even earlier) Canon G15 that is still going strong.
To get it serviced - I took a 5D to Canon some years ago - would probably cost you in the region of around $250, possibly a little extra if you get the sensor cleaned in a proper environment. Make the enquiry first though, as the age of the camera may limit the amount of "support" that Canon are prepared to offer (i.e. they may tell you they won't service it due to the age of it). The same model is available on eBay for prices around the $350 mark, where a Mark III can be purchased second hand for about $550, or new depending on where you look for about $1100 (digital camera warehouse has one here
https://www.digitalcamerawarehouse.c...n-g1x-mark-iii for almost $1400) however it doesn't have the same focal length, the Mark 1 being (from memory) 24-112 mm, and the Mark 3 being 24-72mm) and I've heard that the battery life on the Mark 3 isn't the best. In addition, it was released in 2017, so it's been around for about half as long as the Mark 1.
I'm always reluctant to get rid of a camera that's still working and doing what I ask of it. It depends on your budget, and what the camera is going to be doing. I think in the long run if you're willing to bite the bullet, the Mark 3 has newer technology, but it's not without a few niggles. DP Review did a decent summing up in the conclusion to their review here
https://www.dpreview.com/reviews/can...k-iii-review/7
Hope this is of some help!