Ever since after upgrading from v3 to v4 (probaly many years) ago a lot of the images attached to posts are broken. 

The images are in this format:

 

<img alt="" class="ipsImage" height="750px" src="http://example.com/uploads/post-2039-1237731478.jpg" width="562px">

But for new images the following format is used:

<a class="ipsAttachLink ipsAttachLink_image" href="https://example.com/uploads/attachments/post-2039-1237731478.jpg.beeeee75873f67e2b474d546f407b4dd.jpg"><img class="ipsImage ipsImage_thumbnailed" data-fileid="3430" data-loaded="true" data-ratio="133.33" data-unique="svrp9w9t6" src="https://example.com/uploads/attachments/post-2039-1237731478_thumb.jpg.df0911daccebc42536f7b8e0f064100d.jpg" width="225"></a>

Is there a way of converting these image attachments to the new format? A very simple find-and-replace is not possible because of the unique hash (?) added to each filename. 

All the files are properly converted and still attached to the posts. But not visible.

I've recently paid for license renewal but apparently support is not included anymore... 

There wouldnt be any simple way in which to achieve this. I would suggest employing a developer to assist you with achieving this. It may be worth looking through the providers section for people who offer these services. There are quite a few offering 3.x upgrades

https://invisioncommunity.com/third-party/providers-directory/