Big Problems with Camcorder Tape?

I have been recording a lot of videos off the same tape. I started with a fresh tape, and eventually filled it up. I upload every video to my computer after recording it, so I don't really need to keep buying new tapes when I can just overwrite. I have been overwriting the videos from the begining of the tape, and overwriting those videos from the begining over and over. I've probably made around 40 videos. Most of them have been overwritten from within the first 15 minutes of the tape. Everything used to be fine but lately I have been experiencing some problems.

My videos overlap. If I overwrite an old video by recording a new one over it, later on the video will come back has both combined with a lot of fuzzy random cut outs. It's like watching both videos at the same time, and as you might guess, it doesn't look pretty.

It started doing this for about the first minute of film, but now I noticed it sometimes even goes on for about 5-10 minutes. The only way I can get around this is by filming nothing for about 10 minutes, then coming back and shooting the real film to avoid the 10 minute overlap. Obviously I dont want to continue doing this and I'm afraid soon it will start overlapping for even longer periods of time.

What can I do? I have a fairly old Sony Camcorder (dont know exact name) and I've tried just simply deleting videos, but I can't figure out how. When it says to delete, it says I need a memory card (I dont have one and I dont know what it is)

Any help would be great.