Your DVD player is no longer qualified to match your HD TV, throw it. It is impossible for DVD player to playback 1080p quality movie. Divx you might say? it is not qualified as good HD source even if it is in 1080p format and I doubt the DVD player will output that resolution. Good quality 1080p movie should be about the same size as the original bluray disc (25Gb). What Kratoli said 40Gb for 720p and 90Gb for 1080p is without basis and out of topic. Even dual layer blu-ray disc is only 50Gb and most movies use only 1 layer.
If Blu-ray player is not practical, connect your PC to the TV is the best solution. Depends on the distance between your PC and TV, you may need expensive HDMI cable if the distance is above 20 metres traveling through the ceiling (don't try cheapo long HDMI cable, I have tried that and experienced intermittent signal loss). Another alternative is to buy a media player which is very common nowadays; it supports a lot of formats and is able to output 1080p video and fairly portable.
1 question, is your TV full HD (1080p) or half HD (720p)? TV makers are very smart to cheat consumer by simply put the word "HD" without specifying 720p for non "full HD" TV. If your TV is 720p then the DVD player is still able to serve you well.