Please advice?

To make a long story short, we have used a company in Ukraine to program a complex web page that we have designed. It was supposed to take 3 months, but after over 1 year it is still not finished. The website is 90% ready, but every time they fix a bug they make 10 new bugs - and I do not know if we dare to continue to use them.
I have made a few websites before, but this is the most excruciating experience I’ve ever been through. In addition, the company now want us to pay them the final amount (that was supposed to be paid when the page was finished) + hourly rate of the hours they spend on getting the page ready - even though we have not made any changes in design or content. In addition they write the number of hours with a fork when we compare the number of hours on similar projects that we have worked on earlier.

What I wonder is:
- Is it smart to find a new company to make the site ready, or should I torment myself even more to get them to do the job 100% done?

- Will a new company be skeptical to complete a project that others have developed?

- I reckon that it is an open code that has been used to program the Web site. Can a new company have trouble finish coding the website?

- They have installed the Web page on our dedicated server in USA. Will we need the codes to the web company in Ukraine before a new company can finish programming our Web page? I do not want to pay them the final amount for the completion of the website if they do not finish it.

- I have heard a lot of positive things about programmers in the Philippines. Have any of you experience with freelancers or a company that you can recommend for some advanced projects?

Regards from one who is in the process of developing a large ulcer!

Here's the thing, taking someone else's code and "completing" it is sometimes very difficult because of different coding styles and patterns of thought. I wouldn't just take over a site that someone else has coded, in 99% of the cases it's not nice to work on projects like that and very difficult.

Yes, if it were me I'd tell you to either let me redo the website or I'm not going to touch it with a ten foot pole.

There's no way to tell what language it was written in without looking at the code or some example pages maybe. If it was coded in PHP then yes, a company with PHP experience could take it over, again, if it were my company I wouldn't, but that might just be personal preference.

You will need access to the site's cPanel so that the new developer is able to download the files and database from the server.

Haven't ever had experience with anyone from other countries, I try to rather do everything without outsourcing.