[Solved] Bittorrent stuck on "Connecting to peers", even if it sees and has seeds

I realize that the original format of the post was confusing, so, before you start reading it, here is a summary of solutions. You should read on afterwards in order to understand the context of each solution in part, though:

• Torrents seem to keep a reference to some of the proxy settings when they started downloading. I don't have a clear solution for this, in my case changing the configuration of the proxy and restarting both proxy and Bittorrent eventually solved it. An aggressive solution is to remove all of your torrents and readd them later.
• Sometimes the settings file gets corrupted or the settings don't make a lot of sense. Save all your ongoing downloads, remember all the relevant settings - like download folder -, stop Bittorrent, go to your user's Application Data folder and remove the settings.dat and settings.dat.old files in the Bittorrent folder. (usually C:\Documents and Settings\YourUser\Application Data\Bittorrent or.and C:\Users\YourUser\Application Data\Bittorrent). After restarting Bittorrent you will have a fresh set of settings, so change them to what you need and reload the list of torrents that you saved.
• Check the connection settings. Sometimes you want to minimize the number of connections Bittorrent makes because your provider gives you only a limited connection pool. Make sure the value is not too small. Bittorrent needs a lot of connections: to find peers, to download and upload stuff, to open new connections in order to find the faster one, etc. In my case 15 was too little and I had to restore it to the original 150, even it 15 worked with previous versions of the program.
• Solution from a comment: check your firewall settings and the firewall settings of your router/modem
• Solution from a comment: check your internet provider. Some, like Comcast, are throttling some types of traffic. This link might help: Stop your ISP from Throttling Bittorrent Speeds
• Solution from a comment: enable Bittorrent protocol encryption and restart the application
• Solution from a forum: disable DHT from the Bittorrent client settings (or enable it, if it is disabled?)
• Solution from YouTube: start the torrent client 'As Administrator', suggesting there may be some file access issues you have.
• Solution from a comment: enable DHT. If only some torrents seem to be stuck, see if you can enable DHT in those torrents' properties.

Hope that helps. Now for the original post:

Update (again): While resetting the settings did solve my problem temporarily, I had the same problem the next day as well. The only meaningful thing that I had changed was the global maximum number of connections (Preferences -> Bandwith) from 150, which seemed excessive, to 15. I changed the value back to 150 and it started downloading immediately! This is strange, since the value was 15 for years, I think. Well, I am getting tired of these solutions that only work until the next day. Hopefully this is the last time the problem appears.

Update: The enthusiasm I had after making some of the torrents work faded when I noticed most of the other torrents were still not working. My only solution was to go to the Application Data folder, then Bittorrent, and delete settings.dat and settings.dat.old while the program was closed, then restart Bittorrent. Warning! You will lose all the torrents and settings so save them first (I selected them all and copied the magnet links, then added them back one by one afterwards). The weird thing is that, while it worked, the software also looked quite different from what I was used to. Perhaps just blindly updating the version of Bittorrent all the time is not the best option. Sometimes we need to reset the setting to take advantage of the new software settings.

I've had a problem with a router which prompted me to remove it and put the Internet cable directly into my computer port. I wouldn't recommend it for you, since a router adds a level of protection against outside access, but still, I was not home and a friend of mine "fixed" the problem. Since then, I couldn't download anything on Bittorrent, as it got stuck at "Connecting to peers", even if it connected to the trackers, and saw all the seeds and leechers. Googling around I found a suggestion to remove "resume.dat" from the Bittorrent Application Data folder, but it didn't work for me. I tried a lot of things, but none worked until I found an obscure forum asking about a proxy server. And it dawned on me that it could be from there.
You see, I had previously installed a free proxy program called Privoxy, but I had bound it to the previous IP address of the computer. As a result, it didn't load anymore. The Internet settings were OK, I had removed any reference to a proxy, but strangely enough something in the Bittorrent client kept some information relating to the proxy. After I only bound the proxy to the local address, Privoxy started and miraculously also did the Bittorrent downloads (after a restart of the program).

So, if you have issues with the Bittorent client getting stuck at "Connecting to peers", check if you have recently changed your Internet proxy settings.