*dittos what Veks said*
In regards to the tower, there are number of things that could be wrong depending on other details:
-Does the display show anything at all? If so, what does it say?
-If the desktop beeps, is it a single short beep? Long beep? Series of short beeps? Alternating short/long?
-Is the desktop a 'store' brand (ie. Gateway, Dell, HP, etc) or a custom/local build? If the former, make model info pls? If the latter, you should be able to find the information either on the invoice that came with the computer, the manual that came with it, or if you're comfortable with such, directly on the board itself.
-What does it do after beeping? (ie. turn off automatically, whirr to itself, etc) Does the hard drive light come on or flash?
All that being said, the usual culprits are:
-Loose/dirty video card (pull out, clean contacts, reinsert)
-Loose/dirty mobo component (remove RAM, clean contacts, reinsert; if comfortable with such same with processor, if not, take it to a professional shop to do)
-Dead/failing component (disconnect all drives/peripherals from system bus and power and try a test boot with just the video connected, reconnect one device at a time and test boot after each)
-Insufficient/failing power supply (disconnect drives and test boot or find a similar/more powerful PSU and test)
If you're uncomfortable with playing with the inner workings of a computer, I would strongly encourage finding a local computer shop and paying the fee for a bench test. Usually a competent technician can diagnose and/or repair the issue inside of an hour or two. Depending on where you live and what shop you take it to, a bench test could range from free to $150 or so. Call in advance and see if they can at least give an estimate of how long it would take to find out what the problem is and how much the diagnosis would cost. I would talk to any technical friends you might have and see if they might be willing to look into it or have a shop they could recommend to take it to.
Regarding the laptop...the problem is probably in one of a handful of locations. My concern at the moment is that it sounds like your internal battery is dead completely and it's not getting enough power from the adapter to power up. It could be that you have the wrong power adapter for the laptop or that the power adapter might be dying/dead. I would recommend using a multimeter/voltmeter to test the power adapter. If you don't have one and you don't know anyone that does, you can usually pick up cheapy pocket multimeters at Radio Shack/Home Depot/Lowe's for ~$15 or so. If you're uncomfortable with such, I would recommend taking it into a shop or, possibly, a battery specialist in your area.
Disclaimer: I've worked in IT for over 10 years professionally, varying from local shops to multinational corporations and myriad places in between. The above is based on extremely limited information from the first few posts and may not be close to the problems being experience but founded on years of dealing with PC troubleshooting. While such tips solve perhaps 90% of similar issues, your situation may be radically different from my understanding of the situation. Please consider above information in the way it is intended, an 'educated guess' regarding a computer that is sight unseen but hopefully helpful advice, not as an actual professional diagnosis.