In my understanding - let others correct me - the right way to pinpoint the fault is this:
- put T61 onto a 2504
docking station that exposes LPT port
- attach a motherboard post analyser
- try to boot and watch the number on the analyser
These two lots above are the items which I have purchased with this purpose. You see it's all still theoretical to me..
Now I understand a very common case of T61 fault are dying nVidia video cards. Is yours an nVidia machine?
If the fault is indeed with nVidia card the only way to fix it properly is to replace the video card chip. I understand that if yours is an nVidia 14.1" widescreen machine it should have G86-740-A2 (NVS140M). These can be replaced either with same name - newer date chips or with G86-741-A2 (I understand). Or possibly with other closely named chips.. The process of replacing these chips is known as "BGA rework". I guess you could possibly search for this service locally, within your country or outside of it. Serious laptop repair shops should be offering the service. Phone repair shops might be offering it too but they probably don't have large enough "BGA rework stations" to heat up all of the motherboard. It is highly desirable to heat all of the motherboard to avoid it getting damaged. Some daredevils though have violated this rule and their Thinkpads have lived through it. Respect and applaud to them
I don't know how much the service might cost. I read about a certain guy charging something like £75 somewhere in Russia but that's just one sample and is not representetive. That is for the work I think. The chip on AliExpress costs probably around £12. Nobody really knows how good they are. I've ordered a couple of chips from TaoBao for about £9 a piece but then I got to get them shipped China -> UK for extra charge from the intermediary.. AliExpress seems easier for a one-off purchase.
So assuming it's a video card fault (not guaranteed) you could try to get it fixed. I was considering learning
how do it myself but for me it's a hobby and I'm still a long way from being able to do the work. I guess my aim was to somehow build home herd of functioning T60/T61 and R60/T61 Frankenpad machines with healthy nVidia cards. Don't know why I want it.. It's not like I actually need a herd..
Oh actually it is possible to purchase a replacement motherboard. You know this list
of motherboard FRU-s right? Since yours seems to be 14.1" widescreen only the first section on that page is relevant to you - with six FRU-s in it. They do float on ebay sometimes. There are some on TaoBao. TaoBao is a lot of trouble though - you need an intermediary (superbuy.com or similar) you need app on the phone and you need to ask sellers who advertise the boards if they actually have them. Using google translate if you don't speak Chinese. But it's possible to get a motherboard from them. I got a 14" 4:3 one. I purchased here
and it cost me 150 yuan. See that it's listed at 98 yuan?
That's why you got to talk to them.. Only then will you know if they got one and how much it will cost. Then it's probably up to 100 yuan to have it shipped. I'm suffering 15% markup on currency conversion - part of it is the intermediary fee, part of it is that you got to pay in US dollars only - to superbuy.com at least - and my account is in GBP. So at current exchange rate this should be (150+100)÷9.08×1.15 = £32. Hmm.. if you choose to buy nVidia again it will be again old nVidia so again susceptible to failing..
Yet another option is to purchase a whole 14.1" widescreen T61 or T61p to source the replacement motherboard from it. You obviously don't care what condition the body is in but you care that the motherboard is all right.
On my personal scale 15" 4:3 T60/R60/R61 bodies are valuable and so are T61(p) motherboards fitting them: 14" 4:3 and 15.4" widescreen. I personally attribute less value to 14.1 widescreen machines.. They are of a size where you can get a newer better machine - T400, T410, T500, T510 - hope I'm not inventing names here - or even I dare say to into T*20 or T*30 generation. Their motherboards don't work in 15" 4:3 T60/R60/R61 bodies either.